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


  • Georges Chamoun Ecole centrale de Nantes and Lebanese University.
  • Mazen Saad Ecole centrale de Nantes
  • Raafat Talhouk Lebanese University.



Degenerate parabolic equation, heterogeneous and anisotropic diffusion, global existence of solutions, combined scheme.


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.

Author Biographies

Georges Chamoun, Ecole centrale de Nantes and Lebanese University.

Laboratoire de MathГ©matiques Jean Leray (Nantes,France) et Laboratoire de MathГ©matiques- EDST(Hadath, Liban).

Mazen Saad, Ecole centrale de Nantes

Laboratoire de MathГ©matiques Jean Leray, CNRS UMR 6629, 1 rue de la NoГ©, 44321, Nantes.

Raafat Talhouk, Lebanese University.

Laboratory of Mathematics-EDST and Faculty of Sciences I, Hadath.






Original Articles