A Parabolic Equation of the KPP Type in Higher Dimensions
Jean-François Mallordy, Jean-Michel Roquejoffre
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Source: Crossref
Published: Jan 1, 1995
DOI: 10.1137/s0036141093246105
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The aim of this paper is to study the long-time behaviour of the solutions of a semilinear parabolic equation in an infinite cylinder, which generalises a well-known one-dimensional model that was first investigated by Kolmogorov, Petrovskii, and Piskunov (KPP). It is shown that the asymptotic behaviour of the solutions strongly depends on the asymptotic behaviour of the initial datum at the ends of the cylinder. In particular, the equation admits a continuum of travelling wave solutions, each of them stable with regard to adequate perturbations.
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