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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.

MSC:
92D40 Ecology
35K57 Reaction-diffusion equations
35B10 Periodic solutions to PDEs
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