On Inverse Problems with Pointwise Overdetermination for Mathematical Models of Heat and Mass Transfer

Данная работа - обзор, посвященный обратным задачам восстановления источников и коэффициентов (параметров среды) в математических моделях тепломассопереноса. Главное внимание уделяется вопросам корректности обратных задач с точечными условиями переопределения. Такие вопросы возникают в теории тепломассопереноса, в задачах окружающей среды и экологии, при описании процессов диффузии, фильтрации и во многих других областях. Примерами могут служить задача определения тензора теплопроводности или задача определения источников загрязнения в водном бассейне или атмосфере. Мы рассматриваем три типа задач. Первая из них - задача восстановления точечных или распределенных источников. Описываются условия существования и единственности решений, приводятся примеры неединственности и, в модельных ситуациях, даются оценки на число замеров, которые позволяет полностью определить интенсивности источников и их местоположение. Вторая задача - задача восстановления параметров среды например, теплопроводности. Третья задача - задача о восстановлении граничных режимов, т.е. потока через поверхность или коэффициента теплопередачи.

Ключевые слова

тепломассоперенос; математическое моделирование; параболическое уравнение; обратная задача; единственность; точечный источник.

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