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Lyapunov functionals for a virus dynamic model with general monotonic incidence, two time delays, CTL and antibody immune responses Appl. Math. Lett. (IF 2.9) Pub Date : 2024-07-06 Ke Guo, Donghong Zhao, Zhaosheng Feng
In this paper, we study global asymptotic stability of all equilibria of a virus dynamic model with general monotonic incidence, two time delays, CTL and antibody immune responses by constructing Lyapunov functionals and applying LaSalle’s invariance principle.
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Stability for the magnetic Bénard system with partial dissipation Appl. Math. Lett. (IF 2.9) Pub Date : 2024-07-06 Xiaoping Zhai, Hui Liao, Yajuan Zhao
We prove the stability of the magnetic Bénard system with partial dissipation on perturbations near a background magnetic field in . Neglecting the effect of the temperature, the stability result provides a significant example for the stabilizing effects of the magnetic field on electrically conducting fluids. In addition, we obtain an explicit large-time decay rate of the solutions.
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On boundary conditions for linearised Einstein’s equations Appl. Math. Lett. (IF 2.9) Pub Date : 2024-07-06 Matteo Capoferri, Simone Murro, Gabriel Schmid
We investigate the properties of a fairly large class of boundary conditions for the linearised Einstein equations in the Riemannian setting, ones which generalise the linearised counterpart of boundary conditions proposed by Anderson. Through the prism of the quest to quantise gravitational waves in curved spacetimes, we study their properties from the point of view of ellipticity, gauge invariance
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Travelling waves in a minimal go-or-grow model of cell invasion Appl. Math. Lett. (IF 2.9) Pub Date : 2024-07-04 Carles Falcó, Rebecca M. Crossley, Ruth E. Baker
We consider a minimal go-or-grow model of cell invasion, whereby cells can either proliferate, following logistic growth, or move, via linear diffusion, and phenotypic switching between these two states is density-dependent. Formal analysis in the fast switching regime shows that the total cell density in the two-population go-or-grow model can be described in terms of a single reaction–diffusion equation
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The localized excitation on the Jacobi elliptic function periodic background for the Gross–Pitaevskii equation Appl. Math. Lett. (IF 2.9) Pub Date : 2024-07-03 Xuemei Xu, Yunqing Yang
In this paper, the nonlinear wave solutions for Gross–Pitaevskii equation on the periodic wave background are investigated by Darboux-Bäcklund transformation, from which the soliton and breather wave solutions on the Jacobi elliptic cn and dn functions backgrounds are derived. The corresponding evolutions and dynamical properties of nonlinear wave solutions under different parameters are discussed
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Key-term separation based hierarchical gradient approach for NN based Hammerstein battery model Appl. Math. Lett. (IF 2.9) Pub Date : 2024-06-29 Dongqing Wang
For block-oriented Hammerstein systems with a static nonlinear part and a dynamic linear part, there exists a problem of the parameter coupling in nonlinear part and linear part. Traditional methods are to express its output into a linear or a quasi linear regression equation about parameters. However, a Hammerstein system with a neural network (NN) nonlinear part is difficult to be expressed as a
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Localized waves on the periodic background for the Hermitian symmetric space derivative nonlinear Schrödinger equation Appl. Math. Lett. (IF 2.9) Pub Date : 2024-06-28 Jing Shen, Huan Liu, Fang Li, Xianguo Geng
In this letter, we further investigate the Hermitian symmetric space derivative nonlinear Schrödinger equation through the development of a semi-degenerate Darboux transformation. To demonstrate the utility of this approach, we first reveal the expression of the double-periodic wave solution. On the periodic background, we visualize the kink-breather wave, the rogue wave and their interaction.
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A fast semi-analytical meshless method in two-dimensions Appl. Math. Lett. (IF 2.9) Pub Date : 2024-06-27 Weiwei Li, Bin Wu
This paper introduces a fast direct algorithm for the singular boundary method (SBM) in two-dimensional (2D) problems, utilizing the hierarchical off-diagonal low-rank (HODLR) matrix concept as the foundation of the fast direct solver. The HODLR matrix is constructed by hierarchically partitioning the coefficient matrix into blocks using a binary tree, with all off-diagonal blocks at each level being
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Group analysis and invariant solutions of the (3+1)-dimensional defocusing Gardner-KP equation Appl. Math. Lett. (IF 2.9) Pub Date : 2024-06-26 Xuelin Yong, Jinyu Wu, Xiaozhong Yang
In this paper, the (3+1)-dimensional defocusing Gardner-KP equation is investigated again with the help of Lie symmetry method since the results are either incorrect, or incomplete, or misleading in the literature. For the Lie algebra of infinitesimal symmetries spanned by eight vector fields, the one-dimensional optimal system of subalgebra is established by leveraging the fundamental invariants and
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Two-sided randomized algorithms for approximate [formula omitted]-term t-SVD Appl. Math. Lett. (IF 2.9) Pub Date : 2024-06-26 Xuezhong Wang, Shuai Hou, Kai Wang
This paper is devoted to the computation of the approximate -term t-SVD of third-order tensors via random techniques. With a given truncated term , we obtain the two-side randomized algorithms for the approximate -term t-SVD, denoted by two-sided randomized t-SVD. Furthermore, we delve into the deterministic and probabilistic error bounds, considering specific presumptions regarding the proposed algorithm
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Meshless analysis of fractional diffusion-wave equations by generalized finite difference method Appl. Math. Lett. (IF 2.9) Pub Date : 2024-06-24 Lanyu Qing, Xiaolin Li
In this paper, a meshless generalized finite difference method (GFDM) is proposed to solve the time fractional diffusion-wave (TFDW) equations. A second-order temporal discretization scheme is developed to tackle the Caputo fractional derivative, and then spatial discretization formulas are derived by the GFDM. Theoretical accuracy and convergence of the GFDM for TFDW equations are analyzed. Numerical
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Non-autonomous fractional nonlocal evolution equations with superlinear growth nonlinearities Appl. Math. Lett. (IF 2.9) Pub Date : 2024-06-21 Wei Feng, Pengyu Chen
We carry out an analysis of the existence of solutions for a class of nonlinear fractional partial differential equations of parabolic type with nonlocal initial conditions. Sufficient conditions for the solvability of the desired problem are presented by transforming it into an abstract non-autonomous fractional evolution equation, and constructing two families of solution operators based on the Mittag-Leffler
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A stochastic predator–prey eco-epidemiological model with hunting cooperation Appl. Math. Lett. (IF 2.9) Pub Date : 2024-06-21 Haiqing Zhang, Zijian Liu, Yuanshun Tan, Yu Mu
Cooperative hunting can increase the predator’s hunting ability. In this work, we study a stochastic eco-epidemiological predator–prey model incorporating hunting cooperation. By constructing appropriate auxiliary functions, we establish a sufficient criterion for the existence of a unique ergodic stationary distribution. The findings imply that cooperative hunting has a significant effect on the density
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An adaptive grid method for a two-parameter singularly perturbed problem with non-smooth data Appl. Math. Lett. (IF 2.9) Pub Date : 2024-06-21 Li-Bin Liu, Lei Xu, Yinuo Xu, Zaitang Huang
In this paper, a two-parameter singularly perturbed problem with discontinuous source and convection coefficient is studied. This problem is discretized by using a first-order upwind finite difference scheme for which a posteriori error analysis in the maximum norm is derived. Then, based on this a posteriori error estimation, a grid iteration algorithm is designed to generate an adaptive nonuniform
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Global well-posedness of the 3D damped micropolar Bénard system with horizontal dissipation Appl. Math. Lett. (IF 2.9) Pub Date : 2024-06-17 Hui Liu, Lin Lin, Dong Su, Qiangheng Zhang
In this paper, we consider the global well-posedness of the 3D damped micropolar Bénard system with horizontal dissipation. Global existence and uniqueness of the solution of system (1.1) are proved for and .
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The single-phase solution and Whitham modulation equations of the defocusing self-induced transparency system Appl. Math. Lett. (IF 2.9) Pub Date : 2024-06-15 Yang-Yang Du, Yan-Nan Zhao, Rui Guo
Under investigation in this paper is the defocusing self-induced transparency system which can describe propagation characters of short pulses in Erbium doped fibers with a two-level medium. The single-phase periodic solution and Whitham modulation equations will be derived via finite-gap integration method and Whitham modulation theory. In addition, the oscillatory structure of dispersive shock waves
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A note on the generalized Babuška–Brezzi theory: Revisiting the proof of the associated Strang error estimates Appl. Math. Lett. (IF 2.9) Pub Date : 2024-06-15 Gabriel N. Gatica
In this note we simplify the derivation of the error estimates for the generalized Babuška–Brezzi theory with Galerkin schemes defined in terms of approximate bilinear forms and functionals. More precisely, we provide a straight proof that makes no use of any translated continuous or discrete kernel nor of the distance between them, but of suitable upper bounds of the distances of each component of
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Mean-field derivation of Landau-like equations Appl. Math. Lett. (IF 2.9) Pub Date : 2024-06-09 José Antonio Carrillo, Shuchen Guo, Pierre-Emmanuel Jabin
We derive a class of space homogeneous Landau-like equations from stochastic interacting particles. Through the use of relative entropy, we obtain quantitative bounds on the distance between the solution of the N-particle Liouville equation and the tensorised solution of the limiting Landau-like equation.
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Oscillation criteria for the second-order linear advanced differential equation Appl. Math. Lett. (IF 2.9) Pub Date : 2024-06-08 Zdeněk Opluštil
New oscillatory criteria are established for the second-order linear advanced differential equation. Riccati’s technique and suitable estimates of non-oscillatory solutions are used for the proof of the results obtained. The presented criteria, in a certain sense, generalize the known ones.
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Residual-based a posteriori error estimators for algebraic stabilizations Appl. Math. Lett. (IF 2.9) Pub Date : 2024-06-07 Abhinav Jha
In this note, we extend the analysis for the residual-based a posteriori error estimators in the energy norm defined for the algebraic flux correction (AFC) schemes (Jha, 2021) to the newly proposed algebraic stabilization schemes (John and Knobloch, 2022; Knobloch, 2023). Numerical simulations on adaptively refined grids are performed in two dimensions showing the higher efficiency of an algebraic
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Dynamics of a Lesile–Gower predator–prey model with square root response function and generalist predator Appl. Math. Lett. (IF 2.9) Pub Date : 2024-06-06 Mengxin He, Zhong Li
A Leslie–Gower predator–prey model with square root response function and generalist predator is considered, and the existence and stability of equilibria of the system are discussed. It is shown that the system undergoes a degenerate Hopf bifurcation of codimension exactly two, where there exist two limit cycles. In addition, we find that the system has a cusp of codimension two and exhibits a Bogdanov–Takens
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Existence and Turing instability of positive solutions for a predator–pest model with additional food Appl. Math. Lett. (IF 2.9) Pub Date : 2024-06-06 Jingjing Wang, Yunfeng Jia, Majun Shi
To better explore the dynamics of pests, this paper deals with a brand-new predator–pest model with diffusion and additional food. The existence and diffusion-driven Turing instability of positive constant solutions are discussed. We obtain that for additional food of a certain quality and quantity, there exists a critical value such that the model can produce four forms of positive constant solutions
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On the global existence of solutions to a chemotaxis system with signal-dependent motility, indirect signal production and generalized logistic source Appl. Math. Lett. (IF 2.9) Pub Date : 2024-06-06 Changfeng Liu, Shangjiang Guo
This paper is devoted to a chemotaxis system with signal-dependent motility under homogeneous Neumann boundary conditions in a bounded domain. We prove that this problem possesses a global classical solution which is uniformly bounded under weaker conditions than that obtained by Lv and Wang (2020). The findings of our study demonstrate the presence of a consistent decay rate, effectively ruling out
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Structure preserving FEM for the perturbed wave equation of quantum mechanics Appl. Math. Lett. (IF 2.9) Pub Date : 2024-06-06 Junjun Wang, Rui Chen, Wenjing Ma, Weijie Zhao
The construction and analysis of structure-preserving finite element method (FEM) for computing the perturbed wave equation of quantum mechanics are demonstrated. Firstly, a new fully discrete system is built and proved conservative in the sense of the energy. Meanwhile, the boundedness of the numerical solution is derived. Secondly, the existence and uniqueness of the solution are obtained with the
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Noisy tensor recovery via nonconvex optimization with theoretical recoverability Appl. Math. Lett. (IF 2.9) Pub Date : 2024-06-04 Meng Ding, Jinghua Yang, Jin-Jin Mei
Noisy tensor recovery aims to estimate underlying low-rank tensors from the noisy observations. Besides the sparse noise, tensor data can also be corrupted by the small dense noise. Existing methods typically use the Frobenius norm to handle the small dense noise. In this work, we build a new nonconvex model to decompose the low-rank and sparse components. To be specific, we employ the norm to handle
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AAA rational approximation for time domain model order reduction Appl. Math. Lett. (IF 2.9) Pub Date : 2024-06-03 Giovanni Conni, Frank Naets, Karl Meerbergen
In this paper an extension of the Adaptive Antoulas-Anderson (AAA) Model Order Reduction (MOR) method to time-domain data is defined, referred to as Time-Domain AAA (TDAAA). Inspired by other rational approximation time-domain MOR methods, like Time-Domain Vector Fitting (TDVF) and Time-Domain Loewner Framework (TDLF), TDAAA combines the adaptivity and flexibility of the AAA method in the frequency
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Optimised correction polynomial functions for the Flux Reconstruction method in time-harmonic electromagnetism Appl. Math. Lett. (IF 2.9) Pub Date : 2024-06-01 Matthias Rivet, Sébastien Pernet, Sébastien Tordeux
The Flux Reconstruction (FR) method is classically used in the Computational Fluid Dynamics field. However, its use for the simulation of electromagnetic wave propagation is not as developed yet. Following on from the development of error estimates for the 1D wave equations, we introduce optimisation problems to allow an adaptation of the FR correction polynomial functions to the discretisation parameters
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Stationary Landweber method with momentum acceleration for solving least squares problems Appl. Math. Lett. (IF 2.9) Pub Date : 2024-06-01 Akbar Shirilord, Mehdi Dehghan
In this article, we proposed an enhancement to the convergence rate of Landweber’s method by incorporating the concept of momentum acceleration. Landweber’s method is commonly used to solve least squares problems of the form . Our approach is based on Landweber’s method, which is acknowledged as a particular case of the methodologies outlined in Ding and Chen (2006). Through optimizing the momentum
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Soliton and breather solutions of a reverse time nonlocal coupled nonlinear Schrödinger equation with four-wave mixing effect Appl. Math. Lett. (IF 2.9) Pub Date : 2024-06-01 Jiao Wei, Junyan Wang, Yihao Li
Under investigation is a reverse time nonlocal coupled nonlinear Schrödinger equation with four-wave mixing effect. The -fold Darboux transformation is constructed in a compact determinant representation. As an application, the multi-bright–bright soliton, multi-dark–bright soliton and multi-breather solutions are presented. Dynamical behaviors of the degenerate bright–bright solitons, the regular
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The ultimate boundedness of solutions for stochastic differential equations driven by time-changed Lévy noises Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-31 Qingyan Meng, Yejuan Wang, Peter E. Kloeden, Yinan Ni
The asymptotical ultimate boundedness is established for SDEs driven by time-changed Lévy noises not just in the th moment sense but in the almost sure sense. In particular, we would like to point out that the time-changed process is the inverse of general Lévy subordinators.
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Exotic localized waves in the higher-order nonlinear Schrödinger equation with nonvanishing boundary conditions Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-29 Yongmei Jiang, Xiubin Wang
In this research work, we derive the superregular solitonic solutions of the higher-order nonlinear Schrödinger equation (HNLSE) with nonvanishing boundary conditions by using the dressing method. In order to understand these solutions better, we give the explicit form of one-and two-solitonic solutions and discuss them in detail. This family of novel solutions include Peregrine soliton (PS), Akhmediev
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A note on variable-density flows in porous media Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-27 Michal Beneš
We investigate a fully nonlinear degenerate parabolic system describing variable-density flows of a two-component mixture through porous media. Using the Rothe method of semidiscretization in time we prove the global-in-time existence of weak solutions to the associated initial–boundary value problem under physically reasonable hypotheses on the data, the exponential constitutive equation and the mixed
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Generalization of PINNs for elliptic interface problems Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-27 Xuelian Jiang, Ziming Wang, Wei Bao, Yingxiang Xu
In this letter, we investigate the statistical limits of deep learning for learning solutions of elliptic interface problems from randomly generated data by employing Physics-informed Neural Networks (PINNs). We prove a lower bound and an upper bound for the generalization error of PINNs for solving elliptic interface equations with the Dirichlet boundary condition. In particular, the upper bound on
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Double-pole dark-bright mixed solitons for a three-wave-resonant-interaction system Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-27 Xi-Hu Wu, Yi-Tian Gao
This Letter explores a three-wave-resonant-interaction system that is widely seen in fluid mechanics, plasma physics and nonlinear optics. With the aid of the iterated-form generalized Darboux transformation method, we obtain the second-order analytic solutions that illustrate the double-pole dark-bright mixed solitons. Under certain parameter conditions, the double-pole bright-dark-bright solitons
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On the chemotactic limit of the incompressible chemotaxis-Navier–Stokes equations in [formula omitted] Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-27 Peiguang Wang, Yonghong Wu, Qian Zhang
In this paper, we examine the chemotactic limit of the two-dimensional chemotaxis-Navier–Stokes equations, with a particular emphasis on establishing the rate of convergence as the chemotactic term approaches zero.
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A fast explicit time-splitting spectral scheme for the viscous Cahn–Hilliard equation with nonlocal diffusion operator Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-25 Xinyan Chen, Xinxin Zhang, Leilei Wei, Langyang Huang
The viscous Cahn–Hilliard equation (VCH) is a parameter-dependent model encapsulated Cahn–Hilliard (CH) model and constrained Allen–Cahn (CAC) model. In this paper, we propose a fast explicit time-splitting spectral scheme for the VCH with nonlocal diffusion operator. The numerical scheme is constructed based on the second-order symmetric time-splitting method, which results in a splitting of the original
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Some novel results of a two-community SIR model with asymmetric structure Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-24 Junyuan Yang
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Existence and multiplicity of nontrivial solutions for 1-Superlinear Klein–Gordon–Maxwell system Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-23 Xin Sun, Yu Duan, Jiu Liu
This article concerns the following Klein–Gordon–Maxwell system where is a constant. When satisfies a weaker 1-superlinear condition, existence results for nontrivial solutions and a sequence of high energy solutions are obtained by the Mountain Pass Theorem and Symmetric Mountain Pass Theorem. Our result completes some recent works concerning research on solutions of this system.
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Efficient invariant-preserving scheme for the [formula omitted]-coupled nonlinear Schrödinger equations Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-23 Jiaxiang Cai
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Propagation properties of bright solitons generated by the complex Ginzburg–Landau equation with high-order dispersion and nonlinear gradient terms Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-23 Ziwen Yan, Yuanyuan Yan, Muwei Liu, Wenjun Liu
The asymmetric method is employed to derive the soliton solution for the Ginzburg–Landau complex equation with higher-order dispersion and nonlinear gradient terms. The bright soliton solutions have been obtained and the propagation of solitons has been analyzed. Additionally, the stable transport for the resulting soliton is also provided. And the influence of the initial phase, third-order group
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A note on polynomial-free unisolvence of polyharmonic splines at random points Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-22 Len Bos, Alvise Sommariva, Marco Vianello
In this note we prove almost sure unisolvence of RBF interpolation on randomly distributed sequences by a wide class of polyharmonic splines (including Thin-Plate Splines), without polynomial addition.
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Asymptotic stability of a stochastic Lotka–Volterra competition model with dispersion and Ornstein–Uhlenbeck process Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-21 Qun Liu, Qingmei Chen
To analyze the impacts of dispersion and environmental noise on population dynamics, in the current paper, we propose a stochastic Lotka–Volterra competition model in a patchy environment, where the fluctuations in the varying environment are characterized by an Ornstein–Uhlenbeck process. Besides that, we establish sufficient criteria for the asymptotic stability of the positive equilibrium of the
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Singular solutions for complex second order elliptic equations and their application to time-harmonic diffuse optical tomography Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-20 Jason Curran, Romina Gaburro, Clifford Nolan
We construct singular solutions of a complex elliptic equation of second order, having an isolated singularity of any order. In particular, we extend results obtained for the real partial differential equation in divergence form by Alessandrini in 1990. Our solutions can be applied to the determination of the optical properties of an anisotropic medium in time-harmonic Diffuse Optical Tomography (DOT)
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Maximum bound principle preserving and mass conservative projection method for the conservative Allen–Cahn equation Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-17 Jiayin Li, Jingwei Li, Fenghua Tong
In this paper, we propose and analyze an efficient maximum bound principle (MBP) preserving and mass conservative projection method for the conservative Allen–Cahn equation. The proposed projection operator can be proven contractive in the discrete norm. Discrete MBP and mass conservation are rigorously presented for a second-order exponential time differencing scheme with a central difference discretization
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On saturation of the discrepancy principle for nonlinear Tikhonov regularization in Hilbert spaces Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-16 Qinian Jin
In this paper we revisit the discrepancy principle for Tikhonov regularization of nonlinear ill-posed problems in Hilbert spaces and provide some new and improved saturation results under less restrictive conditions, comparing with the existing results in the literature.
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Discontinuity of the [formula omitted]th eigenvalue for a vibrating beam equation Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-16 Maozhu Zhang, Kun Li, Peijun Ju
The present paper is concerned with the eigenvalues of a problem describing a vibrating beam. The continuity and differentiability of the eigenvalues with respect to the parameters are well understood. Here the discontinuity of the th eigenvalue of the problem is completely characterized. The asymptotic behavior of the th eigenvalue at the discontinuous points and the monotonicity of the th eigenvalue
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Simultaneous uniqueness for the diffusion coefficient and initial value identification in a time-fractional diffusion equation Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-14 Xiaohua Jing, Junxiong Jia, Xueli Song
This article investigates the uniqueness of simultaneously determining the diffusion coefficient and initial value in a time-fractional diffusion equation with derivative order . By additional boundary measurements and a priori assumption on the diffusion coefficient, the uniqueness of the eigenvalues and an associated integral equation for the diffusion coefficient are firstly established. The proof
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Logarithmic type stability for the simultaneous identification of Robin coefficient and heat flux in an elliptic equation Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-14 De-Han Chen, Ting Cheng, Daijun Jiang
In this paper, we aim to reconstruct the unknown Robin coefficient and unknown heat flux simultaneously in an elliptic system from Cauchy data on arbitrarily small portion of accessible boundary. A novel logarithmic type stability in terms of the negative Sobolev norms is established.
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Numerical integration rules based on B-spline bases Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-13 Dionisio F. Yáñez
In this work, we present some new integration formulas for any order of accuracy as an application of the B-spline relations obtained in Amat et al. (2022). The resulting rules are defined as a perturbation of the trapezoidal integration method. We prove the order of approximation and extend the results to several dimensions. Finally, some numerical experiments are performed in order to check the theoretical
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Foundation of the time-fractional beam equation Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-11 Paola Loreti, Daniela Sforza
We derive the model for fractional beam equations by making use of a modified constitutive assumption, that is the relationship between stress and strain depending on the creep compliance given by a fractional power-type function.
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A linear second-order convex splitting scheme for the modified phase-field crystal equation with a strong nonlinear vacancy potential Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-11 Hyun Geun Lee
The modified phase-field crystal (MPFC) equation was extended to the MPFC equation with a strong nonlinear vacancy potential (VMPFC) to include vacancies. In this paper, we develop a linear, second-order, and unconditionally energy stable scheme for solving the VMPFC equation by proposing a new linear convex splitting, using the Crank–Nicolson formula to the contractive part and the second-order Adams–Bashforth
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Modified least squares estimators for Ornstein–Uhlenbeck processes from low-frequency observations Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-11 Yuecai Han, Yaozhong Hu, Dingwen Zhang
We propose a modified least squares estimator for the drift parameter of the Ornstein–Uhlenbeck process when the observations are available at a discrete instant in a low-frequency level. Unlike in the past literature, this modified least squares estimator is asymptotically unbiased. This estimator is combined with the ergodic theorem to obtain joint estimators for both drift and diffusion parameters
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QR decomposition of dual matrices and its application Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-10 Renjie Xu, Tong Wei, Yimin Wei, Pengpeng Xie
Dual number matrix decompositions have played an important role in fields such as kinematics and computer graphics in recent years. In this paper, we present a QR decomposition algorithm for dual number matrices. When dealing with large-scale problems, we present the thin QR decomposition of dual number matrices, along with its algorithm with column pivoting. In numerical experiments, we discuss the
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Boundary blow-up solutions for the Monge-Ampère equation with an invariant gradient type term Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-10 José Francisco de Oliveira, João Marcos do Ó, Pedro Ubilla
We prove existence and non-existence of the boundary blow-up solutions for the Monge–Ampère equation of the form in a smooth, bounded, strictly convex domain , where is positive in , the pair of functions and satisfies conditions of Keller–Osserman type on , and is a quadratic term which is invariant for both the gradient and the Hessian in the sense discussed by Kazdan and Kramer (1978).
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A class of maximum-based iteration methods for the generalized absolute value equation Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-10 Shiliang Wu, Deren Han, Cuixia Li
In this paper, by using , a class of maximum-based iteration methods is established to solve the generalized absolute value equation . Some convergence conditions for the proposed method are presented. By some numerical experiments, the effectiveness and feasibility of the proposed method are confirmed.
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Pressure-robust [formula omitted] error analysis for Raviart–Thomas enriched Scott–Vogelius pairs Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-09 Volker John, Xu Li, Christian Merdon
Recent work shows that it is possible to enrich the Scott–Vogelius finite element pair by certain Raviart–Thomas functions to obtain an inf–sup stable and divergence-free method on general shape-regular meshes. A skew-symmetric consistency term was suggested for avoiding an additional stabilization term for higher order elements, but no error estimate was shown for the Stokes equations. This note closes
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Dynamic analysis of HIV infection model with CTL immune response and cell-to-cell transmission Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-09 Mengfan Tan, Guijie Lan, Chunjin Wei
HIV infection is still a serious worldwide public health problem. During the early stage of HIV infection, the number of infected cells and viruses are extremely low and the process of infection is stochastic. In this paper, we use a stochastic model consisting of continuous-time Markov chain to investigate CTL immune response and two modes of infection (viral transmission and cellular transmission)
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Analysis of solution to an elliptic free boundary value problem equipped with a ‘bad’ data Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-07 Debajyoti Choudhuri, Shengda Zeng
We will study a free boundary value problem driven by a source term which is quite . In the process, we will establish a monotonicity result, and the regularity of solutions to the free boundary value problem under consideration.
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Exact solution of Maxwell–Cattaneo–Vernotte model: Diffusion versus second sound Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-07 J.A.R. Nascimento, A.J.A. Ramos, A.D.S. Campelo, M.M. Freitas
In this work we study the Maxwell–Cattaneo–Vernotte model for heat transport by conduction. We present a methodology to find the exact solution of the model without decoupling the system, so we do not need the restriction . Furthermore, we found a critical value for the thermal relaxation time depending on the physical constants of the system, which allows us to classify heat transport as or . Finally
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Optimal temporal decay rates for 3D compressible magnetohydrodynamics system with nonlinear damping Appl. Math. Lett. (IF 2.9) Pub Date : 2024-05-07 Ruixin Zeng, Shengbin Fu, Weiwei Wang
Recently, Li–Fu–Wang (Li et al., 2022) established the optimal temporal decay rates of solutions near the equilibrium state to the 3D compressible magnetohydrodynamic system with nonlinear damping for . In this paper, we further extend Li–Fu–Wang’s result to the case by finer energy estimates.