Конференции ИВТ СО РАН

Abstracts

The problem of identification of three senior coefficients of the many-dimensional parabolic equation in case of the overdetermination conditions given on three various hyperplanes is studied in this work. The initial inverse problem is reduced to the direct auxiliary problem for the nonlinear integro-differential parabolic equation on the basis of Fourier transform and the overdetermination conditions. The local unique solvability of the obtained direct problem is proved by the method of weak approximation [1] on the basis of the assumption of sufficient smoothness of the initial data. The solution of the original inverse problem is presented in the explicit form through the corresponding solution of the direct problem. The theorem of uniqueness and existence for the classical solution of the inverse problem is proved.

The problems of two coefficients identification in a case when overdetermination conditions are given on two hyperplanes see in [2, 3].

[1]. Белов Ю.Я., Кантор С.А. Метод слабой аппроксимации. Красноярск: КГУ, 1999.

[2]. Белов Ю.Я., Полынцева С.В. Об одной обратной задаче с двумя неизвестными коэффициентами // Тр. III междунар. конф. “Симметрия и дифференциальные уравнения”. Красноярск: Ин-т вычисл. моделирования СО РАН, 2002. с. 60-65.

[3]. Белов Ю.Я., Полынцева С.В. Об одной задаче идентификации двух коэффициентов многомерного параболического уравнения // ДАН. 2004. т. 396. № 5. с. 1-4.

Note. Abstracts are published in author's edition

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