The main goal of this paper is to prove $L^1$-comparison and contraction principles for weak solutions of PDE system corresponding to a phase transition diffusion model of Hele-Shaw type with addition of a linear drift. The flow is considered with a source term and subject to mixed homogeneous boundary conditions: Dirichlet and Neumann. The PDE can be focused to model for instance biological applications including multi-species diffusion-aggregation models and pedestrian dynamics with congestion. Our approach combines DiPerna-Lions renormalization type with Kruzhkov device of doubling and de-doubling variables. The $L^1$-contraction principle allows afterwards to handle the problem in a general framework of nonlinear semigroup theory in $L^1$, thus taking advantage of this strong theory to study furthermore existence, uniqueness, comparison of weak solutions, $L^1$-stability as well as many further questions.

本文的主要目的是证明${\mathrm{大号}}^{\mathrm{1个}}$- 对应于添加线性漂移的 Hele-Shaw 型相变扩散模型的 PDE 系统弱解的比较和收缩原理。流动考虑源项并服从混合均匀边界条件：Dirichlet 和 Neumann。PDE 可以专注于对生物应用程序进行建模，包括多物种扩散聚集模型和拥塞行人动力学。我们的方法将 DiPerna-Lions 重整化类型与加倍和去加倍变量的 Kruzhkov 设备相结合。这${\mathrm{大号}}^{\mathrm{1个}}$-收缩原则允许事后在非线性半群理论的一般框架中处理问题${\mathrm{大号}}^{\mathrm{1个}}$，从而利用这个强理论进一步研究弱解的存在性、唯一性、比较，${\mathrm{大号}}^{\mathrm{1个}}$-稳定性以及许多其他问题。