517.9:532:536 Нелинейные реакционно-диффузионные уравнения с запаздыванием и переменными коэффициентами переноса: решения с обобщенным и функциональным разделением переменных

Полянин А.Д.(Институт проблем механики им. А.Ю. Ишлинского РАН/МГТУ им.Н.Э.Баумана), Журов А.И.(Cardiff University/Институт проблем механики им. А.Ю. Ишлинского РАН)

РЕАКЦИОННО-ДИФФУЗИОННЫЕ УРАВНЕНИЯ С ЗАПАЗДЫВАНИЕМ, ПЕРЕМЕННЫЕ КОЭФФИЦИЕНТЫ ПЕРЕНОСА, ТОЧНЫЕ РЕШЕНИЯ, РЕШЕНИЯ С ОБОБЩЕННЫМ РАЗДЕЛЕНИЕМ ПЕРЕМЕННЫХ, РЕШЕНИЯ С ФУНКЦИОНАЛЬНЫМ РАЗДЕЛЕНИЕМ ПЕРЕМЕННЫХ, ПЕРЕМЕННОЕ ЗАПАЗДЫВАНИЕ, НЕЛИНЕЙНЫЕ УРАВНЕНИЯ В ЧАСТНЫХ ПРОИЗВОДНЫХ С ЗАПАЗДЫВАНИЕМ


doi: 10.18698/2309-3684-2015-4-337


Описан ряд новых точных решений с простым, обобщенным и функциональным разделениями переменных одномерных нелинейных реакционно-диффузионных уравнений с запаздывающим аргументом и переменными коэффициентами переноса. Все представленные уравнения содержат одну, две или три произвольные функции одного аргумента. Решения с обобщенным разделением переменных находят в виде , где функции определяют в ходе анализа с использованием новой модификации метода функциональных связей. Некоторые из результатов обобщены на случай нелинейных реакционно-диффузионных уравнений с переменным запаздыванием. Также представлены точные решения более сложных трехмерных реакционно-диффузионных уравнений с запаздыванием. Большинство полученных решений содержат свободные параметры и могут быть использованы для решения некоторых задач, а также для тестирования приближенных аналитических и численных методов решения нелинейных уравнений в частных производных с запаздыванием.


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Полянин А. Д., Журов А. И. Нелинейные реакционно-диффузионные уравнения с запаздыванием и переменными коэффициентами переноса: решения с обобщенным и функциональным разделением переменных. Математическое моделирование и численные методы, 2015, №4 (8), c. 3-37



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