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Zbl 1180.35098
Tian, Canrong; Lin, Zhigui; Pedersen, Michael
Instability induced by cross-diffusion in reaction-diffusion systems. (English)
[J] Nonlinear Anal., Real World Appl. 11, No. 2, 1036-1045 (2010). ISSN 1468-1218

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 2000:
*35B35 Stability of solutions of PDE
35K57 Reaction-diffusion equations
35K45 Systems of parabolic equations, initial value problems

Keywords: pattern formation; unbounded domain; bounded domain

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