Sharp asymptotics for the multidimensional KPP equation
type: Item
instance of: scholarly article
title: Sharp asymptotics for the multidimensional KPP equation
zbMATH Open document ID: 0994.35021
DOI: 10.1016/S0304-4149(99)00039-3
author: R. Smith
published in: Stochastic Processes and their Applications
publication date: 2002-08-29T00:00:00Z
review text: The authors investigate asymptotics of solutions of the nonhomogeneous Kolmogorov-Petrovskij-Piskunov equation depending on a small parameter \(\varepsilon \to 0\): \[ {\partial u^\varepsilon \over \partial t}(t,x)={\varepsilon ^2\over 2}\Delta u^\varepsilon + {c(x)\over \varepsilon ^2} u^\varepsilon (1-u^\varepsilon), \quad x\in \mathbb{R}^d, \] complemented with the initial condition \(u^\varepsilon (0,x)={\mathbf 1}_A(x)\), the characteristic function of the set \(A\) which determines the initial position of the wave front. Here \(c\in C^3(\mathbb{R}^d)\) is a nonnegative function, \(c(x)\leq C(1+|x|)\). The dependence of the asymptotics on the geometry of the boundary of \(A\) is precisely described for the problem with constraints.
reviewed by: Hana Petzeltová
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 1792539
zbMATH Keywords: large deviations
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1792539