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On the regularization Cauchy problem for matrix factorizations of the Helmholtz equation in a multidimensional bounded domainстатья
Дата последнего поиска статьи во внешних источниках: 20 апреля 2022 г.
- Авторы: Juraev D.A., Gasimov Y.S.
- Журнал: Azerbaijan Journal of Mathematics
- Том: 12
- Номер: 1
- Год издания: 2022
- Первая страница: 142
- Последняя страница: 161
- Аннотация: In this paper, the problem of continuation of the solution of the ill-posedCauchy problem for matrix factorizations of the Helmholtz equation in a multidimensional bounded domain is considered. It is assumed that the solution to the problemexists and is continuously differentiable in a closed domain with exactly given Cauchydata. For this case, an explicit formula for the continuation of the solution is established,as well as a regularization formula for the case where, under the indicated conditions,instead of Cauchy data their continuous approximations with a given error in uniformmetric are given. A stability estimate for the solution of the Cauchy problem in theclassical sense is obtained.
- Добавил в систему: Жураев Даврон Аслонкулович