A Representation of Solution of the Identification Problem of the Coefficients at Second Order Operator in the Multi-Dimensional Parabolic Equations System
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https://elib.sfu-kras.ru/handle/2311/10142Author:
Romanenko, Galina V.
Романенко, Галина В.
Date:
2014-01Abstract:
An identification problem of the coefficients at differential operator of second order and sum of lowest
terms in system of multidimensional parabolic equations with Cauchy data was studied in this article. The
theorems of existence and uniqueness of the solution for direct and inverse problems have been proved.
The method of weak approximation is used to the proof existence of solutions Исследована обратная задача с данными Коши для системы многомерных параболических урав-
нений, содержащих неизвестные коэффициенты перед дифференциальным оператором второго
порядка по выделенной переменной и суммой младших членов. Начальные данные имеют специ-
альный вид и заданы в виде произведения двух функций, зависящих от разных переменных. Полу-
чены достаточные условия существования и единственности решения вспомогательной прямой
и исходной обратной задач. Для доказательства используется метод слабой аппроксимации
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