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Global boundedness in a two-species predator-prey chemotaxis model. (English) Zbl 1450.35087

Summary: This paper is devoted to investigate the global boundedness of a two-species predator-prey chemotaxis model with one signal. By establishing the uniform boundedness of \(L^2\)-norm for prey and predator densities and the uniform boundedness of \(L^4\)-norm for the signal gradient, we consider the global existence and boundedness of classical solutions to the model in a three-dimensional bounded domain.

MSC:

35B45 A priori estimates in context of PDEs
35K51 Initial-boundary value problems for second-order parabolic systems
35K59 Quasilinear parabolic equations
92D25 Population dynamics (general)
92C17 Cell movement (chemotaxis, etc.)
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