This article deals with the following singular parabolic–elliptic chemotaxis system (0.1)ut=Δu−χ∇⋅(uv∇v),x∈Ω,0=Δv−αv+μu,x∈Ω,under homogeneous Neumann boundary conditions in a smooth bounded domain Ω⊂RN with N≥3, where parameters χ,α and μ are positive constants. Fujie, Winkler, and Yokota Fujie(2015) in 2014 and Fujie and Senba Fujie(2016) in 2016 proved that system (0.1) has a unique globally bounded

We study two-crested traveling Stokes waves on the surface of an ideal fluid with infinite depth. Following Chen & Saffman (1980), we refer to these waves as class II Stokes waves. The class II waves are found from bifurcations from the primary branch of Stokes waves away from the flat surface. These waves are strongly nonlinear, and are disconnected from small-amplitude solutions. Distinct class II

In this paper, a new framework for studying the existence of generalized or strongly generalized solutions to a wide class of inclusion systems involving double-phase, possibly competing differential operators, convection, and mixed boundary conditions is introduced. The technical approach exploits Galerkin’s method and a surjective theorem for multifunctions in finite dimensional spaces.

In the paper, we complement existing oscillation criteria for linear third-order delay differential equations by establishing novel sufficient conditions for the nonexistence of so-called Kneser solutions (nonoscillatory solutions with alternating signs of their derivatives). The significant extent of our improvement over known results is illustrated by the example provided. Furthermore, the technique

The cusp singularity, with only Hölder continuity, is a typical singularity formed in the quasilinear hyperbolic partial differential equations, such as the Hunter–Saxton and Camassa–Holm equations. We establish the global existence of Hölder continuous energy conservative weak solution for a family of Hunter–Saxton type equations, where the regularity of solution varies with respect to a parameter

In this paper, we investigate the Cauchy problem for a new integrable nonlocal fifth-order nonlinear Schrödinger (FONLS) equation with three free parameters. By solving a 2 × 2 matrix Riemann–Hilbert problem in the complex k-plane, we obtain the limit form solutions of the nonlocal FONLS equation. As an example, we provide an exact expression of the one-soliton solution for the nonlocal FONLS equation

In this paper, our main purpose is to prove the existence of the first eigenvalue for the polyharmonic operator with Navier boundary conditions. In addition, the corresponding eigenfunction is demonstrated to be positive. As an application, we will discuss a necessary condition for the existence of positive solutions to some polyharmonic problems on the first eigenvalue.

This paper explores the asymptotic profile of steady states in a partially degenerate Aedes aegypti population model within advective environments. By reducing the model to a scalar equation, we establish the existence and uniqueness of positive steady-state solutions using the method of upper and lower solutions. We analyze the interaction between diffusion and advection, focusing on their effects

In this paper, we propose conservative Crank–Nicolson-type and compact finite difference schemes for the nonlinear Schrödinger equation with point nonlinearity. To construct these schemes, we first transform the point nonlinearity into an interface condition, then decompose the computational domain along the interface into two subregions with a jump condition. Different discretization approximations

This note considers the computation of the logarithm of symmetric positive definite matrices using the Gauss–Legendre (GL) quadrature. The GL quadrature becomes slow when the condition number of the given matrix is large. In this note, we propose a technique dividing the matrix logarithm into two matrix logarithms, where the condition numbers of the divided logarithm arguments are smaller than that

In this work, we propose and analyze a stochastic SIQRS epidemic model with the disease transmission rate driven by a log-normal Ornstein–Uhlenbeck process. By establishing a series of Lyapunov functions, we derive sufficient criteria for the asymptotical stability of the positive equilibrium of the system which suggests the prevalence of the disease in the long term. This work provides a basis for

We consider the absolute value equation (AVE) Ax−|x|=b, where the diagonal entries of A∈Rn×n are all greater than 1 and 〈A〉−I is an irreducible singular M-matrix (〈A〉 is the comparison matrix of A). We investigate the existence and uniqueness of solutions for the AVE. The AVE does not necessarily have a unique solution for every b∈Rn, so most of the existing convergence results for various iterative

The paper investigates a pivotal condition for the Bobkov-Tanaka type spectrum for double-phase operators. This condition is satisfied if either the weight w driving the double-phase operator is strictly positive in the whole domain or the domain is convex and fulfils a suitable symmetry condition.

This study refines the two-stage social insect model of Kang et al. (2015) by incorporating a nonlinear egg cannibalism rate. The introduction of nonlinearity presents analytical challenges, addressed through the application of the compound matrix method to rigorously establish global stability. The analysis reveals complex dynamical behaviors, including two distinct types of bistability: one between

We consider a nonlinear eigenvalue problem driven by the nonautonomous (p,q)-Laplacian with unbalanced growth. Using suitable Rayleigh quotients and variational tools, we show that the problem has a continuous spectrum which is an upper half line and we also show a nonexistence result for a lower half line.

How does the delay function affect its decay rate for a stable stochastic delay differential equation with an unbounded delay? Under suitable Khasminskii-type conditions, an existence-and-uniqueness theorem for an SDDE with a general unbounded time-varying delay will be firstly given. Its decay rate will be discussed when the equation is stable. Given the unbounded delay function, it will be shown

In this paper, we consider the oscillation of second-order neutral advanced dynamic equations on time scales of the form (r(t)(zΔ(t))α)Δ+q(t)f(y(m(t)))=0, where z(t)=y(t)+p(t)y(τ(t)) and m(t)≥t. We consider two cases of τ(t)≥t and τ(t)≤t, respectively. Some new oscillatory results are based on the new comparison theorems that enable us to reduce problem of the oscillation of the second-order equations

This paper presents a multi-scale method for inhomogeneous fourth-order singular perturbation problems. This method guarantees a uniform high-order convergence rate, regardless of the presence of multi-scale coefficients or boundary layer effects. The numerical experiments in two and three dimensions confirm the theory.

A fast wavelet collocation method with compression techniques is proposed for solving the Steklov eigenvalue problem. Based on the potential theory, the Steklov eigenvalue problem is reformulated as a boundary integral equation with logarithmic singularity. By using the compression technique, the wavelet coefficient matrix is truncated into sparse. This technique leads to the algorithm faster. We show

This study presents a normalized time-fractional Fisher equation to resolve scaling inconsistencies associated with conventional time-fractional derivatives. A finite difference scheme is applied to numerically solve the equation. Computational experiments are conducted to investigate the impact of the fractional order on the system’s dynamics. The numerical results demonstrate the influence of memory

The fundamental solution is a particular solution of the inhomogeneous equation with Dirac delta function as the right hand side term. It holds significant importance in both applied and theoretical mathematics and physics. This study focuses on deriving 3D fundamental solutions in the frequency domain for wave propagation in a fluid-saturated porous medium in the context of Biot's theory. The approach

The method of complex variable functions is integrated to investigate the steady state problem wherein SH guided waves impinge upon two dimensional layered inhomogeneous piezoelectric media with a circular inclusion, and the corresponding analytical expressions are derived. Specifically, the guided wave expansion technique is employed to formulate the incident wave field of planar SH guided waves.

In numerical linear algebra, finding the low-rank approximation of large-scale nonsymmetric matrices is a core problem. In this work, we combine the generalized Nyström method and randomized subspace iteration to propose a new low-rank approximation algorithm, which we refer to as the generalized Nyström method with subspace iteration. Moreover, utilizing the projection theory, we perform an in-depth

In this paper, we consider a viscous compressible two-fluid model with a pressure law that depends on two variables. We establish the existence theory for the global solution of this system within the HN(R3)-framework (N≥2), assuming that the H2(R3)-norm of the initial perturbation is small. The energy method combined with the low-frequency and high-frequency decomposition is used to derive the decay

Kacamarz-type inner-iteration preconditioned flexible GMRES method, which was proposed by Du et al. (2021), is attractive for solving consistent linear systems. However, its inner iteration was only performed by several commonly used Kaczmarz-type methods, and required computing AAT in advance, which is unfavorable for big data problems. To overcome these difficulties, we first propose a simple orthogonal

In this paper, we propose and analyze a nonautonomous, nonlinear size-structured population model that describes the growth and division of cells. By applying the monotone method based on a comparison principle, we establish the well-posedness of the model. We then investigate the long-term behavior of the solution using the upper–lower solution approach. Specifically, we derive conditions on the model

A mesoscopic lattice Boltzmann model is proposed to investigate the dynamic evolution of solid-state structures during the hexagonal-to-orthorhombic transition, incorporating the micro-elastic theory. The model enables detailed observation of the morphology of both single- and multi-variant systems. The analytically recovered macroscopic governing equation is fully consistent with the kinetic theory

In this paper, we propose one novel generalized finite difference method(GFDM) for the moving beams and plates problem. Firstly the second-order backward difference formula scheme is used for the time discretization. And the GFDM idea is explored to discrete the space area. The proposed method is easy to code and deal with the complex boundary conditions. The convergence test is presented and agrees

This study concentrates on exact solutions on the Jacobian elliptic function periodic background to the variable-coefficient nonlinear Schrödinger (vcNLS) equation. Through constructing the new eigenvalue solution for Lax pair and using the known Darboux transformation (DT) of vcNLS equation, the breather and rogue wave (RW) structures on Jacobian elliptic function backgrounds are revealed. By changing

This paper addresses the global existence and boundedness of classical solutions to the Neumann-Neumann-Dirichlet value problem for the chemotaxis system, as described by (*)nt+u⋅∇n=Δn−χ∇⋅n1+c∇c+∇⋅(n∇ϕ),x∈Ω,t>0,ct+u⋅∇c=Δc−nαc,x∈Ω,t>0,ut+∇P=Δu−n∇ϕ+n1+c∇c,x∈Ω,t>0,∇⋅u=0,x∈Ω,t>0∂n∂ν=∂c∂ν=0,u=0,x∈∂Ω,t>0n(x,0)=n0(x),c(x,0)=c0(x),u(x,0)=u0(x),x∈Ωin a smoothly bounded domain Ω⊂RN(N=2,3), where α>0 and the

The known mathematical model of Glassy-winged Sharpshooter, described by a nonlinear differential equation with delay, is considered under a combination of stochastic perturbations of the type of white noise and Poisson’s jumps. It is assumed that stochastic perturbations are directly proportional to the deviation of the system state from the positive equilibrium. Via the general method of Lyapunov

The uniqueness of global weak solutions to one-dimensional doubly degenerate cross-diffusion system is shown. The equations model the evolution of feeding bacterial populations in a malnourished environment. The key idea of the proof is applying anti-derivative of the sum of weak solutions to the system.

For the Wasserstein-1 metric matrices of one- and two-dimensions, we prove the two guesses about their computational properties, which were proposed by Bai in 2024 (Linear Algebra Appl. 681(2024), 150-186). More specifically, for these matrices we prove their nonsingularity and symmetric positive definiteness, and derive sharper upper bounds on the norms of their inverses and on their condition numbers

The current article focuses on the quasi-exponential stability analysis of non-autonomous integro-differential systems characterized by infinite delay. By developing a novel generalized Halanay inequality, sufficient conditions for the quasi-exponential stability of non-autonomous integro-differential systems with infinite delay are presented for the systems.

This paper considers a nonlocal reaction–diffusion model with a non-monotone birth pulse and a bistable response term. We define two monotone semiflows and, using the comparison argument, obtain the threshold dynamics between persistence and extinction in bounded domain. Moreover, we apply the asymptotic fixed point theorem to show the existence of bistable traveling wave solutions.

In this letter, we derive the sharp-interface limit of the Cahn–Hilliard–Biot equations using formal matched asymptotic expansions. We find that in each sub-domain, the quasi-static Biot equations are obtained with domain-specific material parameters. Moreover, across the interface, material displacement and pore pressure are continuous, while volumetric fluid content and normal stress are balanced

This paper introduces a hybrid numerical method for simulating two- and three-dimensional nonlinear transient heat conduction problems with temperature-dependent thermal conductivity over extended time intervals. The approach employs the Krylov deferred correction method for temporal discretization, which is particularly effective for dynamic simulations requiring high accuracy. After temporal discretization

In this paper, the well-posedness and asymptotic behavior of a non-local lattice system are analyzed in the space ℓ1. In fact, the analysis is carried out in the subspace ℓ+1 formed by the nonnegative elements, remaining open the case of the whole space. The same problem has been analyzed recently in the space ℓ2 (see Y. Li et al., Communications on Pure and Applied Analysis, 23 (2024), 935-960). However

This paper deals with a singular chemotaxis system with logistic source and non-sublinear production under homogeneous boundary condition: ut=Δu−χ∇⋅(uv∇v)+ru−μuk, vt=Δv−v+uβ in a bounded convex domain Ω⊂Rn with n≥1, here χ,μ>0, r∈R, k>1 and β≥1. It is proved that the system admits a global solution if k>2 with β∈[1,k−1), or k>1 and β≥1 with χ≤4nβ2. Moreover, the solution is globally bounded for the

As a continuation of Wang (2024), in the present paper, we consider the following problem in RN−Δu+V(x)u=λ(−ix⊥⋅∇u)+μu+|u|pu,u∈H1(RN,ℂ),∫RN|u|2dx=m>0,Re∫RN(−ix⊥⋅∇uu¯)dx=l∈R,where N=2 or N=3, x⊥ is the magnetic potential (see Introduction). When lm∉Z, 2

This paper is concerned with the spatial propagation of cooperative systems with general diffusions including multiple types of nonlocal dispersal mechanisms. We show the diversity of long-term behavioral patterns exhibited by different components within these systems, under the assumption that the diffusion operator bring about infinite spreading speed in propagation dynamics. Specifically, we observe

This note investigates the formation of singularities for the 3D Navier–Stokes equations. By employing a bilinear estimate and a logarithmic interpolation inequality, we derive a new extension criterion based on two vorticity components in Vishik-type spaces, which refines several previously established results concerning Navier–Stokes equations.

This paper is devoted to investigate a discrete Nicholson’s blowflies model with two delays. We construct some novel upper and lower solutions for the wave equation and then show the equation admits the traveling wave fronts connecting two equilibria of the associated spatially homogeneous system. And also, we obtain the non-existence for traveling waves of the model.

This paper is concerned with the minimal wave speed of exclusion traveling wave solutions in a delayed competitive systems. Because of the intraspecific delays, the system cannot generate monotone semiflows. We give the minimal wave speed by combining different recipes. Here, the minimal wave speed is linearly determinate.

Balanced-norm error bounds have been established in Cheng et al. (2022) for the local discontinuous Galerkin (LDG) method using alternating numerical flux on Shishkin-type meshes. However, the convergence rate is shown to be one-half order lower than the numerical results in the general case. This paper seeks to fill up this gap by introducing a new composite projector in the error analysis. We achieve

A two-component generalization of the Camassa–Holm equation and its reduction proposed recently by Xue, Du and Geng [Appl. Math. Lett. 146 (2023) 108795] are studied. For this two-component equation, its missing bi-Hamiltonian structure is constructed and a Miura transformation is introduced so that it may be regarded as a modification of the very first two-component Camassa–Holm equation. Using a

In this paper, we investigate the Hartree–Fock type system: −Δu+λu+μϕu,vu=uq−2u+ρvq2uq2−2u,−Δv+λv+μϕu,vv=vq−2v+ρuq2vq2−2v,where ϕu,v(x)=∫R3u2(y)+v2(y)|x−y|dy, the parameters μ,ρ>0 and q∈(2,3). Such a system is regarded as an approximation of the Coulomb system of two particles that occurs in quantum mechanics. Due to the existence of the nonlocal term ϕu,v, we find that in R3, the energy of the minimizer

We construct in this paper an efficient spectral Galerkin approximation in combination with scalar auxiliary variable (SAV) method to the Allen–Cahn model and Cahn–Hilliard model in polar geometry. Since the spectral methods cannot be directly applied to the non-rectangular regions, the disk region is firstly mapped to the rectangular region by the polar transformation that will lead to singularity

In this paper, we study solitary waves for the geophysical Green–Naghdi (gGN) system which describing the propagation of large amplitude surface waves. We give a description of the solitary wave profiles by performing a phase-plane analysis, and present explicit solitary wave solutions. The results reveal the influence of the relationship between the Coriolis parameter and wave speed on the existence

In this paper, we study the nonexistence of global weak solutions for a wave equation with nonlinear memory and damping terms. We give an answer to an open problem posed in D’Abbicco (2014). Moreover, comparing with the existing results, our results do not require any positivity condition of the initial values. The proof of our results is based on the asymptotic properties of solutions for an integral

In this work, Hamiltonian variational principle is employed to prove that Schrödinger–Maxwell (SM) equations under Lorenz gauge exhibit a symplectic structure. Based on this, symplectic mixed spectral element time domain method (S-MSETD) for SM equations under Lorenz gauge is proposed. This method is a structure-preserving geometric algorithm that achieves high accuracy, particularly in long-term simulation

Inverse source problems frequently occur in real-world applications, such as pinpointing the location of contaminant sources in areas that are difficult to access. In this paper, we consider an inverse source problem of identifying an unknown source term in an abstract fractional diffusion-wave equation with inexact order. Due to the ill-posed nature of the problem, we propose a truncation method to

A hierarchy of lattice equations, including a coupled five-point lattice equation, is proposed. By employing the zero-curvature equation, Lax pairs for this hierarchy are derived from a 4 × 4 linear matrix spectral problem. Subsequently, the Hamiltonian structure of the hierarchy is established using the trace identity. Furthermore, infinitely many conservation laws for the coupled five-point lattice

The dynamics of viscous thin-film particle-laden flows down inclined surfaces are commonly modeled with one of two approaches: a diffusive flux model or a suspension balance model. The diffusive flux model assumes that the particles migrate via a diffusive flux induced by gradients in both the particle concentration and the effective suspension viscosity. The suspension balance model introduces non-Newtonian

We give a new blowup criterion for the strong solution of Cauchy problem for three-dimensional micropolar fluid equations with vacuum. It shows that the strong or smooth solution exists globally if the L∞(0,T:Lq)-norm of the density is bounded, where q is a positive constant. Particularly, we succeed in removing the technical condition ρ0∈L1 in Hou and Xu (2024).

This paper is devoted to the study of the combined effects of impulsive harvesting and small advection on the dynamical behavior of solutions to a free boundary model. By introducing a one-parameter family of initial data σϕ with σ≥0 and ϕ being a compactly supported function, under some suitable assumptions, we obtain a threshold value σ∗ such that spreading happens when σ>σ∗, vanishing happens when

Taking advantage of the reproducing kernel theory, several effective numerical algorithms have been developed to solve boundary value problems (BVPs) with the exact right side functions. However, these methods have difficulty in solving effectively linear boundary value problems when the right side of the equation has contaminated data. The objective of this letter is to introduce a robust numerical

In Noor et al. (2011), the second-order Taylor expansion of the objective function is incorrectly used in constructing the descent direction. Thus, the proposed block coordinate descent method is non-monotone and a strict convergence analysis is lack. This motivates us to propose a monotone block coordinate descent method for solving absolute value equations. Under appropriate conditions, we analyze

In this paper, we investigate an HIV latent infection model that incorporates cell-to-cell transmission and multiple drug classes, extending the model proposed by Areej Alshorman et al. (2022). We derive the basic reproduction number R0 for the model and establish the existence and local stability of its equilibria. By constructing appropriate Lyapunov functions, we analyze the global stability of

In this article, we propose and analyze the finite element method for the mixed Stokes–Darcy–Darcy system which involves free flow in conduits coupled with confined flow in fractured porous media. The interactions on the interfaces come from the classical Stokes–Darcy system and the famous bulk-fracture system. Rigorously theoretical results are derived and some numerical results are provided to verify