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On the well posedness and further regularity of a diffusive three species aquatic model. (English) Zbl 1252.35153

Summary: We consider Upadhay’s three species aquatic food chain model, with the inclusion of spatial spread. This is a well established food chain model for the interaction of three given aquatic species. It exhibits rich dynamical behavior, including chaos. We prove the existence of a global weak solution to the diffusive system, followed by existence of local mild and strong solution.

MSC:

35K51 Initial-boundary value problems for second-order parabolic systems
35K58 Semilinear parabolic equations
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35D30 Weak solutions to PDEs
35D35 Strong solutions to PDEs
92D25 Population dynamics (general)
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