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Analysis of a parabolic cross-diffusion population model without self-diffusion. (English) Zbl 1096.35060
The authors study the global existence of nonnegative weak solutions to a strongly coupled parabolic system. The existence proof is based on a positivity-preserving backward Euler-Galerkin approximation, discrete entropy estimates, and L 1 weak compactness arguments.
Reviewer: Jiaqi Mo (Wuhu)
MSC:
35K50Systems of parabolic equations, boundary value problems (MSC2000)
35K55Nonlinear parabolic equations
35K57Reaction-diffusion equations
92D25Population dynamics (general)