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 J. Sib. Fed. Univ. Math. Phys., 2016, Volume 9, Issue 2, Pages 180–191 (Mi jsfu475)

An identification problem of nonlinear lowest term coefficient in the special form for two-dimensional semilinear parabolic equation

Ekaterina N. Kriger, Igor V. Frolenkov

Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041, Russia

Abstract: In this paper we investigate an identification problem of a coefficient at the nonlinear lowest term in a 2D semilinear parabolic equation with overdetermination conditions given on a smooth curve. The unknown coefficient has the form of a product of two functions each depending on time and a spatial variable. We prove solvability of the problem in classes of smooth bounded functions. We present an example of input data satisfying the conditions of the theorem and the corresponding solution.

Keywords: inverse problem, semilinear parabolic equation, Cauchy problem, lowest term coefficient, weak approximation method, local solvability, overdetermination conditions on a smooth curve.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 14.Y26.31.0006 The research for this paper was carried out in Siberian Federal University within the framework of the project «Multidimensional Complex Analysis and Differential Equations» funded by the grant of the Russian Federation Government to support scientific research under supervision of a leading scientist, no. 14.Y26.31.0006.

DOI: https://doi.org/10.17516/1997-1397-2016-9-2-180-191

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UDC: 517.9
Received in revised form: 16.02.2016
Accepted: 18.03.2016
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Citation: Ekaterina N. Kriger, Igor V. Frolenkov, “An identification problem of nonlinear lowest term coefficient in the special form for two-dimensional semilinear parabolic equation”, J. Sib. Fed. Univ. Math. Phys., 9:2 (2016), 180–191

Citation in format AMSBIB
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