On Evolutionary Inverse Problems for Mathematical Models of Heat and Mass Transfer

Представлены результаты о корректности обратных задач для математических моделей тепломассопереноса. Неизвестными являются правая часть в уравнении (функция источников) и коэффициенты уравнения. Условия переопределения - значения решения на некоторых многообразиях или в отдельных точках. Рассматриваются два класса математических моделей. Первая включает систему уравнений Навье - Стокса, дополненную параболическим уравнением для температуры и параболической системой для концентраций примесей. Правая часть неизвестна и характеризует объемную плотность источников в жидкости. Неизвестные функции зависят от времени и части пространственных переменных и входят в правую часть уравнения. Второй класс систем - параболическая система уравнений уравнений для концентраций переносимых веществ, где неизвестные входят как в правую часть так и саму систему в качестве коэффициентов. Показана корректность этих задач, в частности полученные теоремы существования, единственности и оценки устойчивости для решений. Далее, мы опишем некоторые алгоритмы решения обратных задач о восстановлении точечных источников по точечным данным переопределения, основанные на асимптотике решений функций Грина соответствующих эллиптических задач.

Ключевые слова

обратная задача; тепломассообмен; фильтрация; диффузия; корректность.

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