论文标题
熵结构保存交叉扩散系统的时空公式：分析和盖尔金离散
An entropy structure preserving space-time formulation for cross-diffusion systems: Analysis and Galerkin discretization
论文作者
论文摘要
交叉扩散系统是非线性抛物线偏微分方程的系统，用于描述几种应用中的动态过程，包括化学浓度和细胞生物学。我们提出了一种时空方法，以证明跨扩散系统的有界弱解的存在，从而利用系统熵来检查长期行为，并证明该解决方案是非负性的，即使没有最大原则。这种方法自然产生了一种新型的时空盖尔金方法，用于保存其熵结构的交叉扩散系统的数值近似。我们证明了离散溶液的存在和收敛，并为多孔介质，Fisher-KPP和Maxwell-Stefan问题提供了数值结果。
Cross-diffusion systems are systems of nonlinear parabolic partial differential equations that are used to describe dynamical processes in several application, including chemical concentrations and cell biology. We present a space-time approach to the proof of existence of bounded weak solutions of cross-diffusion systems, making use of the system entropy to examine long-term behavior and to show that the solution is nonnegative, even when a maximum principle is not available. This approach naturally gives rise to a novel space-time Galerkin method for the numerical approximation of cross-diffusion systems that conserves their entropy structure. We prove existence and convergence of the discrete solutions, and present numerical results for the porous medium, the Fisher-KPP, and the Maxwell-Stefan problem.
