On Exact Solutions of a Multidimensional System of Elliptic Equations with Power-Law Nonlinearities

被引：2

作者：

Kosov, A. A. ^{[1
]}

Semenov, E. I. ^{[1
]}

机构：

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

来源：

DIFFERENTIAL EQUATIONS | 2023年 / 59卷 / 12期

基金：

俄罗斯科学基金会;

关键词：

POSITIVE SOLUTIONS; DIFFUSION;

D O I：

10.1134/S0012266123120054

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Equations and systems of elliptic type with power-law nonlinearities are considered. Such equations are found in modeling distributed robotic formations, as well as in chemical kinetics, biology, astrophysics, and many other fields. The problem of constructing multidimensional exact solutions is studied. It is proposed to use a special type of ansatz that reduces the problem to solving systems of algebraic equations. A number of multiparameter families of new exact multidimensional solutions (both radially symmetric and anisotropic) represented by explicit formulas are obtained. Examples are given to illustrate the exact solutions found.

引用

页码：1627 / 1649

页数：23

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