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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.

UDC: 517.9

Received: 10.12.2015
Received in revised form: 16.02.2016
Accepted: 18.03.2016

Language: English

DOI: 10.17516/1997-1397-2016-9-2-180-191

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