DIFFUSION-WAVE TYPE SOLUTIONS WITH TWO FRONTS TO A NONLINEAR DEGENERATE REACTION-DIFFUSION SYSTEM

被引：3

作者：

Kazakov, A. L. ^{[1
]}

Spevak, L. F. ^{[2
]}

机构：

[1] Russian Acad Sci, Inst Syst Dynam & Control Theory, Siberian Branch, Irkutsk 664033, Russia

[2] Russian Acad Sci, Gorkunov Inst Engn Sci, Ural Branch, Ekaterinburg 620049, Russia

来源：

JOURNAL OF APPLIED MECHANICS AND TECHNICAL PHYSICS | 2022年 / 63卷 / 06期

基金：

俄罗斯基础研究基金会;

关键词：

reaction-diffusion system; diffusion wave; existence and uniqueness theorem; power series; radial basis functions; BOUNDARY-VALUE PROBLEM;

D O I：

10.1134/S0021894422060128

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

Diffusion-wave type solutions are constructed and investigated for a nonlinear parabolic reaction-diffusion system. The statement of the problem in which mismatched zero fronts are set for different desired functions is considered for the first time. The existence and uniqueness theorem of solutions in the form of series in a class of piecewise analytic functions is proven. It is proposed to construct the desired type of approximate solutions using a step-by-step iterative algorithm based on the collocation method and expansion in radial basis functions. Calculations are performed, and the results of these calculations are verified using the series segments. The behavior of the constructed solutions is numerically analyzed.

引用

页码：995 / 1004

页数：10

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