Veronica Anaya, Mostafa Bendahmane, Mauricio Sepúlveda:
Numerical analysis for HP food chain system with nonlocal and cross diffusion
In this paper, we consider a reaction-diffusion system describing three interacting species in the HP food chain structure with nonlocal and cross diffusion. We construct a finite volume scheme for this system, we establish existence and uniqueness of the discrete solution, and it is also showed that the scheme converges to the corresponding weak solution for the model studied. The convergence proof is based on the use of the discrete Sobolev embedding inequalities with general boundary conditions and a space-time $L^1$ compactness argument that mimics the compactness lemma due to S. N. Kruzhkov. Finally we give some numerical examples.
This preprint gave rise to the following definitive publication(s):
Veronica ANAYA, Mostafa BENDAHMANE, Mauricio SEPúLVEDA: Numerical analysis for a three interacting species model with nonlocal and cross diffusion. ESAIM: Mathematical Modelling and Numerical Analysis, vol. 49, 1, pp. 171-192, (2015).