Traveling-Wave Solutions of the Kolmogorov-Petrovskii-Piskunov Equation

被引：9
|
作者：
Pikulin, S. V. [1 ]
机构：
[1] Russian Acad Sci, Dorodnicyn Comp Ctr, Fed Res Ctr Comp Sci & Control, Moscow 119333, Russia
来源：
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2018年 / 58卷 / 02期
基金：
俄罗斯基础研究基金会;
关键词：
Kolmogorov-Petrovskii-Piskunov equation; generalized Fisher equation; Abel's equation of the second kind; Fuchs-Kowalewski-Painleve test; self-similar solutions; traveling waves; intermediate asymptotic regime; MODELS;
D O I：
10.1134/S0965542518020124
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider quasi-stationary solutions of a problem without initial conditions for the Kolmogorov-Petrovskii-Piskunov (KPP) equation, which is a quasilinear parabolic one arising in the modeling of certain reaction-diffusion processes in the theory of combustion, mathematical biology, and other areas of natural sciences. A new efficiently numerically implementable analytical representation is constructed for self-similar plane traveling-wave solutions of the KPP equation with a special right-hand side. Sufficient conditions for an auxiliary function involved in this representation to be analytical for all values of its argument, including the endpoints, are obtained. Numerical results are obtained for model examples.
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页码：230 / 237
页数：8
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