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Instability induced by cross-diffusion in reaction-diffusion systems. (English) Zbl 1180.35098
Summary: The instability of the uniform equilibrium of a general strongly coupled reaction-diffusion is discussed. In an unbounded and a bounded domain, sufficient conditions for instability are obtained, respectively. The conclusion is applied to the ecosystem, it is shown that cross-diffusion can induce the instability of an equilibrium which is stable for the kinetic system and for the self-diffusion-reaction system.
MSC:
35B35Stability of solutions of PDE
35K57Reaction-diffusion equations
35K45Systems of second-order parabolic equations, initial value problems
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