Тип публикации: статья из журнала
Год издания: 1995
Идентификатор DOI: 10.1515/jiip.1995.3.1.83
Аннотация: — This work is to examine the existence and uniqueness of solutions to problems of determining the source function in the heat equation when the sought-for function depends on all independent variables of the equation. We have found sufficient conditions for unique solvability of these problems. We examine the well-posedness of proПоказать полностьюblems of source identification in a parabolic equation under various overdetermining conditions. The problem of determining the source function in a parabolic equation has been considered by many authors (see, e.g. [1-4,6,8-12,14,15]). They generally assume that the sought-for function is independent of one or more variables of the equation. In this work, we do not impose this constraint: The unknown source is a function of all independent variables. We obtain sufficient conditions for unique solvability of such problems and give examples demonstrating that the problems may have more than one solution when the conditions are violated. © 1995, Walter de Gruyter. All rights reserved.
Журнал: Journal of Inverse and Ill-Posed Problems
Выпуск журнала: Vol. 3, Is. 1
Номера страниц: 83-102