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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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Online
ISSN
1569-3945
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Volume 20, Issue 5-6

Issues

On some identification problem for source function to one semievolutionary system

Yuri Y. Belov / Vera G. Kopylova
Published Online: 2012-12-14 | DOI: https://doi.org/10.1515/jip-2011-0027

Abstract.

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 , we prove the following: the solvability “in general” of the inverse problem for , uniqueness of classical solutions of the inverse problem, periodicity of the spatial variable solutions of approximating problems for , a priori (uniform in ) 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 , the rate of convergence (order ) 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).

Keywords: Identification; inverse problem; parabolic equation; initial conditions; overdetermination conditions; the method of weak approximation; a small parameter; convergence

About the article

Received: 2011-08-25

Published Online: 2012-12-14

Published in Print: 2012-12-01


Citation Information: , Volume 20, Issue 5-6, Pages 723–743, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jip-2011-0027.

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© 2012 by Walter de Gruyter Berlin Boston.Get Permission

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