Raimund Bürger, Rafael Ordoñez, Mauricio Sepúlveda, Luis M. Villada:
Numerical analysis of a three-species chemotaxis model
A reaction-diffusion system is formulated to describe three interacting species within the Hastings-Powell (HP) food chain structure with chemotaxis produced by three chemicals. The existence of a weak solution is proven and a finite volume (FV) scheme for this system is constructed. In combination with the non-negativity and the a priori estimate, the existence of a discrete solution of the FV scheme is proven, and it is shown that the scheme converges to the corresponding weak solution of the model. The convergence proof uses two ingredients of interest for various applications, namely the discrete Sobolev embedding inequalities with general boundary conditions and a space-time L^1 compactness argument. Finally, numerical tests illustrate the model and the behavior of the FV scheme.
This preprint gave rise to the following definitive publication(s):
Raimund BüRGER, Rafael ORDOñEZ, Mauricio SEPúLVEDA, Luis M. VILLADA: Numerical analysis of a three-species chemotaxis model. Computers & Mathematics with Applications, vol. 80, pp. 183-203, (2020).