On the Concept of Index for Partial Differential Algebraic Equations Arising in Modelling of Processes in Power Plants
DOI:
https://doi.org/10.14529/mmp170201Ключевые слова:
дифференциально-алгебраические уравнения, частные производные, интегро-дифференциальные уравнения, пространство решений, индекс, модели энергетических установок.Аннотация
В статье рассматриваются некоторые классы линейных и квазилинейных дифференциально-алгебраических уравнений (ДАУ) в частных производных. ПодДАУ в частных производных в работе понимаются системы с вырожденными во всей области определения матрицами при старших производных искомой вектор-функции. Они не являются системами типа Коши - Ковалевской, и утверждения о разрешимости в общем случае отсутствуют. Конкретным объектом изучения являются эволюционные системы с одной пространственной переменной. Проведены исследования ДАУ высокого порядка, зависящих от параметра. На этой основе введено понятие индекса ДАУ в частных производных. Рассмотрены постановки начально-краевых задач для ДАУ в частных производных. Полученные результаты применяются для анализа моделей процессов тепломассообмена в энергетических установках.
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