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Zbl 1096.35060
Chen, Li; Jüngel, Ansgar
Analysis of a parabolic cross-diffusion population model without self-diffusion. (English)
[J] J. Differ. Equations 224, No. 1, 39-59 (2006). ISSN 0022-0396

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.
[Jiaqi Mo (Wuhu)]

MSC 2000:: *35K50 Systems of parabolic equations, boundary value problems
35K55 Nonlinear parabolic equations
35K57 Reaction-diffusion equations
92D25 Population dynamics

Keywords: population equations; strong cross-diffusion; weak competition; relative entropy; global-in-time existence of weak solutions; long-time behavior of solutions

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Zentralblatt MATH Berlin [Germany]