Mathematical and numerical analysis of an acid-mediated cancer invasion model with nonlinear diffusion

Abstract

In this paper, we study the existence of weak solutions of the nonlinear cancer invasion parabolic system with density-dependent diffusion operators. To establish the existence result, we use regularization, the Faedo-Galerkin approximation method, some a priori estimates, and compactness arguments. Furthermore in this paper, we present results of numerical simulations for the considered invasion system with various nonlinear density-dependent diffusion operators. A standard Galerkin finite element method with the backward Euler algorithm in time is used as a numerical tool to discretize the given cancer invasion parabolic system. The theoretical results are validated by numerical examples.