Сибирский федеральный университет

Тип публикации: статья из журнала

Год издания: 2012

Идентификатор DOI: 10.1515/jip-2011-0027

Ключевые слова: Identification, inverse problem, parabolic equation, initial conditions, overdetermination conditions, the method of weak approximation, a small parameter, convergence, Overdetermination, Parabolic Equations, Weak approximation, Identification (control systems), Inverse problems, Parameter estimation, Partial differential equations, Problem solving

Аннотация: We solve an identification problem for source functions to one-dimensional second order parabolic-elliptic system. Considered the system of equations obtained from the original system, where the time derivative added to the elliptic equation, containing a small parameter epsilon > 0, we prove the following: the solvability "in general" of the inverse problem for epsilon > 0, uniqueness of classical solutions of the inverse problem, periodicity of the spatial variable solutions of approximating problems for epsilon > 0, a priori (uniform in epsilon > 0) estimates of solutions of approximating problems, convergence on the basis of the a priori estimates of solutions approximating the inverse problems to solutions original for epsilon -> 0, the rate of convergence (order O(epsilon(1/2))) of solutions of approximating problems in classes of continuous functions. An identification problem of source functions in the system of composite type is treated by some authors. The case where the unknown component of the vector source function in the equation that does not contain the small parameter was studied by Belov (2010).

Журнал: JOURNAL OF INVERSE AND ILL-POSED PROBLEMS

Выпуск журнала: Vol. 20, Is. 5-6

Номера страниц: 723-743

ISSN журнала: 09280219

Место издания: BERLIN

Издатель: WALTER DE GRUYTER & CO

• Belov Y.Y. (Institute of Mathematics,Siberian Federal University)
• Kopylova V.G. (Institute of Mathematics,Siberian Federal University)

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