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Reaction-diffusion-advection models for the effects and evolution of dispersal. (English) Zbl 1277.35002

Summary: This review describes reaction-advection-diffusion models for the ecological effects and evolution of dispersal, and mathematical methods for analyzing those models. The topics covered include models for a single species, models for ecological interactions between species, and models for the evolution of dispersal strategies. The models are all set on bounded domains. The mathematical methods include spectral theory, specifically the theory of principal eigenvalues for elliptic operators, maximum principles and comparison theorems, bifurcation theory, and persistence theory.

MSC:

35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
35K57 Reaction-diffusion equations
92D40 Ecology
35J61 Semilinear elliptic equations
35R09 Integro-partial differential equations
92D15 Problems related to evolution
35K58 Semilinear parabolic equations
35B32 Bifurcations in context of PDEs
35K51 Initial-boundary value problems for second-order parabolic systems
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