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Analysis of the periodically fragmented environment model. II: Biological invasions and pulsating travelling fronts. (English) Zbl 1083.92036
Summary: This paper is concerned with propagation phenomena for reaction-diffusion equations of the type: \(u_{t}-\bigtriangledown (A(x)\bigtriangledown u)= f(x,u)\), \(x \in \mathbb R^{N}\), where \(A\) is a given periodic diffusion matrix field, and \(f\) is a given nonlinearity which is periodic in the \(x\)-variables. This article is the sequel to the authors’ paper, J. Math. Biol. 51, No. 1, 75–113 (2005; Zbl 1066.92047). The existence of pulsating fronts describing the biological invasion of the uniform zero state by a heterogeneous state is proved. A variational characterization of the minimal speed of such pulsating fronts is proved and the dependency of this speed on the heterogeneity of the medium is also analyzed.

92D40 Ecology
35K57 Reaction-diffusion equations
35B10 Periodic solutions to PDEs
Full Text: DOI
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