Mathematical and Numerical Analysis of a Modified Keller-Segel Model with General Diffusive Tensors.

• Main Authors: Georges Chamoun, Mazen Saad, Raafat Talhouk
• Format: Article
• Language: English
• Published: Biomath Forum 2013-12-01
• Series: Biomath
• Subjects: Degenerate parabolic equation; heterogeneous and anisotropic diffusion; global existence of solutions; combined scheme.
• Online Access: http://www.biomathforum.org/biomath/index.php/biomath/article/view/194

This paper is devoted to the mathematical analysis of a model arising from biology, consisting of diffusion and chemotaxis with volume filling effect. Motivated by numerical and modeling issues, the global existence in time and the uniqueness of weak solutions to this model is investigated. The novelty with respect to other related papers lies in the presence of a two-sidedly nonlinear degenerate diffusion and anisotropic heterogeneous diffusion tensors, where we prove global existence and uniquenessunder further assumptions. Moreover, we introduce and we study the convergence analysis of the combined scheme applied to this anisotropic Keller-Segel model with general tensors. Finally, a numerical test is given to prove the effectiveness of the combined scheme.