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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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An inverse problem for a system of evolution equations

1Sobolev Institute of Mathematics, Koptyug prosp. 4, Novosibirsk, 630090, Russia.

2Department of Mathematics, University of Science and Technology of China, 96 Jinzhai Road, Hefei, Anhui, 230026, P. R. China.

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 19, Issue 1, Pages 1–12, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/jiip.2011.020, May 2011

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In this paper, we consider an inverse problem for a system of evolution equations. The inverse problem can also be interpreted as a exact control problem in the transition of a substance W(x, t) from a nonlocal state W 1(x) to another nonlocal state W 2(x). The control element is assumed to have a nonlocal form. We show the existence of the inverse problem in classes of entire functions with respect to the spatial variable by the constructive method. Explicit formulas of the unknown functions W(x, t) and λ(x) are presented.

Keywords.: Inverse problem; evolution equations; exact control problem; nonlocal state

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