Pattern formation for a reaction diffusion system with constant and cross diffusion

Abstract

In this work, we study a finite volume scheme for a reaction diffusion system with constant and cross diffusionmodeling the spread of an epidemic disease within a host population structured with three subclasses of individuals (SIR-model). The mobility in each class is assumed to be influenced by the gradient of other classes. We establish the existence of a solution to the finite volume scheme and show convergence to a weak solution. The convergence proof is based on deriving a series of a priori estimates and using a general Lp compactness criterion.