Inverse Problems for Some Sobolev-Type Mathematical Models
Ключевые слова:
модели соболевского типа, уравнение Соболева, математическая модель, теорема существования и единственности решения, обратная задача, краевая задача, волны в плазме, вращающаяся жидкость, модель Буссинеска - Лява.Аннотация
Работа посвящена рассмотрению обратных задач для ряда математических моделей, основанных на уравнениях и системах Соболевского типа, возникающих в динамике стратифицированной жидкости, теории упругости, гидродинамике, электродинамике и других областях. Вместе с решением определяются неизвестная правой части и коэффициенты в уравнении типа Соболева четвертого порядка. В качестве условия переопределения берутся значения решения в отдельных точках пространственной области. Задача сводится к некоторому операторному уравнению, разрешимость которого устанавливается при помощи априорных оценок и теоремы о неподвижной точке.Доказываются теоремы о существовании и единственности решения поставленной задачи для линейного и нелинейного случая. В линейном случае результат является глобальным по времени, а в нелинейном локальным по времени. В качестве основных пространств рассматриваются пространства С.Л. Соболева.
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