Страница публикации

Reduction Method and New Exact Solutions of the Multidimensional Nonlinear Heat Equation

Тип публикации: Статья в журнале

Тип материала: Текст

Авторы: Kosov A.A., Semenov E.I.

Журнал: Differential Equations

Язык публикации: english

Том: 58

Номера страниц: 187-194

Количество страниц: 8

Номер: 2

Год публикации: 2022

Отчетный год: 2022

DOI: 10.1134/S0012266122020057

Аннотация: A nonlinear multidimensional heat equation with a power-law coefficient is studied. It isproposed to construct its exact solutions by the multidimensional reduction method based on theuse of a special ansatz. As a result of the reduction, the problem is reduced to solving systems ofmatrix-vector algebraic equations that determine the dependence on the spatial variables andintegrating ordinary differential equations that determine the dependence on time. For a numberof examples with various values of the exponents, explicit expressions are obtained in terms ofelementary functions for exact multidimensional solutions, including those anisotropic in thespatial variables. The exact solutions found can be useful when constructing approximatesolutions of boundary value problems for the nonlinear heat equation using numerical methodsleading to the need to solve high-dimensional systems of equations.

Индексируется WOS: Q3

Индексируется Scopus: Нет

Индексируется УБС: Нет

Индексируется РИНЦ: Да

Индексируется ВАК: Нет

Индексируется CORE: Нет