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Mathematical Notes

, Volume 106, Issue 3–4, pp 378–389 | Cite as

Inverse Problems of Finding the Absorption Parameter in the Diffusion Equation

  • A. I. KozhanovEmail author
Article
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Abstract

The paper is devoted to the study of inverse problems of finding, together with a solution u(x, t) of the diffusion equation
$${u_t} - \Delta u + [c(x,t) + a{q_0}(x,t)]u = f(x,t),$$
the parameter a characterizing absorption (c(x,t) and q0(x,t) are given functions). It is assumed that, on the function u(x,t), nonpercolation conditions and some special overdetermination conditions of integral form are imposed. We prove existence theorems for solutions (u(x,t),a) such that the function u(x, t) has all Sobolev generalized derivatives appearing in the equation and a is a nonnegative number.

Keywords

diffusion equation nonpercolation condition unknown parameter inverse problems final integral overdetermination conditions existence 

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Notes

Funding

This work was supported by the Russian Foundation for Basic Research under grant 18-01-00620.

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsSiberian Branch of Russian Academy of SciencesNovosibirskRussia

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