Kolmogorov-Petrovskii-Piskunov方程行波渐近解的收敛性

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Theoretical and Mathematical Physics Pub Date : 2025-04-25 DOI:10.1134/S0040577925040038

L. A. Kalyakin

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引用次数: 0

摘要

对于半线性抛物型偏微分方程，我们考虑一个收敛于大倍行波\(t\)的渐近解。这种波的速度是时变的，我们将其渐近性构造为\(t\to\infty\)。我们发现渐近包含对数，不能以幂级数的形式构造。

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Asymptotic solution convergence to a traveling wave in the Kolmogorov–Petrovskii–Piskunov equation

For a semilinear parabolic partial differential equation, we consider an asymptotic solution that converges to a traveling wave at large times \(t\). The velocity of such a wave is time dependent, and we construct the asymptotics as \(t\to\infty\). We find that the asymptotics contains logarithms and cannot be constructed in the form of a power series.

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来源期刊

Theoretical and Mathematical Physics 物理-物理：数学物理

CiteScore

1.60

自引率

20.00%

发文量

103

审稿时长

4-8 weeks

期刊介绍： Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems. Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.