Solvability and numerical simulations for tumor invasion model with nonlinear diffusion. Issue 2 (7th November 2019)

• Record Type: Journal Article
• Authors: Manimaran, Jeyaraj; Shangerganesh, Lingeshwaran
• Is Part Of: Computational and mathematical methods. Volume 2:Issue 2(2020)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2019-11-07
• Subjects: cancer invasion -- H+ ions -- nonlinear diffusion -- weak solution; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Periodicals; Numerical analysis; Mathematics -- Data processing; Periodicals; 004.0151
• DOI: 10.1002/cmm4.1068
• Languages: English
• ISSNs: 2577-7408

Abstract

Abstract : This paper is devoted to study the nonlinear diffusion parabolic partial differential equations, which describes the invasion of cancer cells into the normal tissues. We prove the existence of a weak solution of the considered model using the Faedo‐Galerkin approximation method, a priori estimates, and compactness arguments. Then, the considered model is discretized in space with the standard Galerkin finite elements and in time with the Crank‐Nicolson method. Furthermore, nonlinear terms in the proposed model is treated semi‐implicitly in the finite element scheme. Numerical results are validated by convergence study and existing numerical results of similar problems. Finally, the influence of nonlinear diffusion is studied to understand the effect in the cancer invasion model.