Volume 52, pp. 576-598, 2020.

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

L. Shangerganesh and J. Manimaran


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.

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Key words

cancer invasion, density-dependent diffusion, Faedo-Galerkin approximation, finite element method

AMS subject classifications

35D30, 65M60, 35K57

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