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Optimization analysis of the inverse coefficient problem for the nonlinear convection-diffusion-reaction equation

  • Roman V. Brizitskii EMAIL logo and Zhanna Y. Saritskaya
Published/Copyright: May 29, 2018

Abstract

The inverse coefficient problem for the nonlinear convection-diffusion-reaction equation is considered. A velocity vector and a mass-transfer coefficient are considered as the unknown coefficients and are recovered with the help of the additional information about the boundary value problem’s solution. The inverse coefficient problem is reduced to a two-parameter problem of multiplicative control, the solvability of which is proved in a general form. For a cubic reaction coefficient the local stability estimates of the control problem’s solutions are obtained regarding to a rather small perturbation of either the cost functional or the specified functions of the boundary value problem.

MSC 2010: 35A05

Award Identifier / Grant number: 16-01-00365-a

Award Identifier / Grant number: 18-5-064

Funding statement: The first author was supported by the Federal Agency for Scientific Organizations in framework of the state task (subject no. 0263-2018-0001). The second author was supported by the Russian Foundation for Basic Research (project no. 16-01-00365-a) and by the Fundamental Research Program FEB RAS “Far East” (project no. 18-5-064).

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Received: 2017-01-20
Revised: 2018-05-06
Accepted: 2018-05-06
Published Online: 2018-05-29
Published in Print: 2018-12-01

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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