Analysis of a Multidimensional Parabolic Population Model with Strong Cross-Diffusion

Abstract. The global existence of a non-negative weak solution to a multi-dimensional parabolic strongly coupled model for two competing species is proved. The main feature of the model is that the diffusion matrix is non-symmetric and generally not positive definite and that the non-diagonal matrix elements (the cross-diffusion terms) are allowed to be “large”. The ideas of the existence proof are a careful approximation of the cross-diffusion terms using finite differences and the use of an entropy inequality yielding a priori estimates.