Nonlinear partial differential equations with delay: linear stability/instability of solutions, numerical integration

被引：2

作者：

Sorokin, V. G. ^{[1
,2
]}

Polyanin, A. D. ^{[1
,2
,3
]}

机构：

[1] Russian Acad Sci, Ishlinsky Inst Problems Mech, Moscow, Russia

[2] Bauman Moscow State Tech Univ, Moscow, Russia

[3] Natl Res Nucl Univ MEPhI, Moscow, Russia

来源：

VII INTERNATIONAL CONFERENCE PROBLEMS OF MATHEMATICAL PHYSICS AND MATHEMATICAL MODELLING | 2019年 / 1205卷

基金：

俄罗斯基础研究基金会;

关键词：

partial differential equations with delay; delay reaction-diffusion equations; exact solutions; stability and instability of solutions; numerical integration; REACTION-DIFFUSION EQUATIONS; FUNCTIONAL CONSTRAINTS METHOD; SEPARABLE SOLUTIONS; NEURAL-NETWORKS; STABILITY;

D O I：

10.1088/1742-6596/1205/1/012053

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The paper deals with partial differential equations of parabolic and hyperbolic types that contain a nonlinear kinetic function with delay. Conditions for the linear stability and instability of stationary solutions of reaction-diffusion equations and conditions for the instability of solutions of more complicated equations with delay are formulated. A nonstationary solution of the model initial-boundary value problem with delay and quadratic nonlinearity is investigated for stability/instability. A numerical solution of the test problem in the domain of stability is obtained by the method of lines.

引用

页数：7

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