Global Existence of Solutions to a Cross-Diffusion System in Higher Dimensional Domains
We consider a strongly coupled nonlinear parabolic system which arises from population dynamics in N-dimensional (N ≥ 1) domains. We establish global existence of classical solutions under certain restrictions on diffusion coefficients, self-diffusion coefficients and cross-diffusion coefficients for both species.
& Zhao, C.
(2005). Global Existence of Solutions to a Cross-Diffusion System in Higher Dimensional Domains. Discrete and Continuous Dynamical Systems - Series A (DCDS-A), 12 (2), 185-192.