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Mat. Zametki, 2017, Volume 101, Issue 6, Pages 860–870 (Mi mz11370)  

On the Stabilization to Zero of the Solutions of the Inverse Problem for a Degenerate Parabolic Equation with Two Independent Variables

V. L. Kamynin

National Engineering Physics Institute "MEPhI", Moscow

Abstract: Theorems on the stabilization to zero as $t\to +\infty$ of solutions of the inverse problem of determining the unknown right-hand side of a degenerate parabolic equation with one space variable belonging to a bounded closed interval are proved under an integral observation condition. Further, it is assumed that the coefficients of the equation are unbounded. These theorems can be used to obtain an upper bound for the stabilization rate. The paper contains examples of equations for which the assumptions of the theorems hold, as well as an example showing that such assumptions are essential.

Keywords: degenerate parabolic equation, asymptotic behavior, inverse problem.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 02.a03.21005
This work was supported by the Program for Increasing the Competitiveness of NRNU MEPhI (grant no. 02.a03.21005 of 27.08.2013).


DOI: https://doi.org/10.4213/mzm11370

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English version:
Mathematical Notes, 2017, 101:6, 974–983

Bibliographic databases:

UDC: 517.95
PACS: 02.30.Zz
Received: 26.03.2016

Citation: V. L. Kamynin, “On the Stabilization to Zero of the Solutions of the Inverse Problem for a Degenerate Parabolic Equation with Two Independent Variables”, Mat. Zametki, 101:6 (2017), 860–870; Math. Notes, 101:6 (2017), 974–983

Citation in format AMSBIB
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