Русская версия
ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

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The Method of Solving the Inverse Problem for the Evolution Equation with a Superstable Semigroup

Author(s):

Ivan Vladimirovich Tikhonov

Doctor of Physical and Mathematical Sciences,
Professor of Department of Mathematical Physics,
Faculty of Computational Mathematics and Cybernetics,
Lomonosov Moscow State University

ivtikh@mail.ru

Vu Nguyen Son Tung

Postgraduate Student of Mathematical Analysis Department,
Moscow State University of Education.
Post and Office Address:
Mathematical Analysis Department,
Moscow State University of Education,
Krasnoprudnaya Str., 14,
Moscow, Russia, 107140.

vnsontung@mail.ru

Abstract:

The paper presents an extended description of the report which was made at the scientific conference «Herzen Readings — 2017». The linear inverse problem for the evolution equation in a Banach space is studied. It is required to recover a unknown nonhomogeneous term. Additional information is given in the form of a nonlocal condition with the Riemann-Stieltjes integral. For conducting research a special assumption related to the superstability of the evolution semigroup is introduced. It is shown that the solution of the inverse problem can be represented by a convergent Neumann series. As a result, a constructive method for finding a solution of the inverse problem has been obtained. The case when the Neumann series becomes a finite sum is singled out separately. A model example of the inverse problem with final overdetermination is considered.

Keywords

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