An identification problem of coefficient for two-dimensional semilinear parabolic equation with the Cauchy data


Тип публикации: статья из журнала

Год издания: 2015

Идентификатор DOI: 10.3103/S1066369X15050035

Ключевые слова: Cauchy problem, coefficient at lowest term, existence and uniqueness of solution, inverse problem, semilinear parabolic equation, weak approximation method

Аннотация: In this paper we consider the problem of identification of coefficient at nonlinear lowest term for two-dimensional semilinear parabolic equation. The desired coefficient depends on all variables and has the form of the sum of two functions each of them depends on time and on a spatial variable. The indicated inverse problem is redПоказать полностьюuced to non-classical direct problem which contains the traces of unknown function and its derivatives. The investigation of existence and uniqueness of solution of the auxiliary direct problem is carried out by means of the weak approximation method. We prove theorems of existence and uniqueness of the inverse problem solution in classes of smooth bounded functions. We present an example of input data satisfying the conditions of the proved theorems and corresponding solution. © 2015, Allerton Press, Inc.

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Журнал: Russian Mathematics

Выпуск журнала: Vol. 59, Is. 5

Номера страниц: 17-31


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