Inverse Coefficient Problems for Nonlinear Parabolic Differential Equations

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Ou Y. H., Hasanov A., Liu Z. H.

ACTA MATHEMATICA SINICA-ENGLISH SERIES, vol.24, no.10, pp.1617-1624, 2008 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 24 Issue: 10
• Publication Date: 2008
• Doi Number: 10.1007/s10114-008-6384-0
• Journal Name: ACTA MATHEMATICA SINICA-ENGLISH SERIES
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Page Numbers: pp.1617-1624
• Kocaeli University Affiliated: Yes

Abstract

This paper is devoted to a class of inverse problems for a nonlinear parabolic differential equation. The unknown coefficient of the equation depends on the gradient of the solution and belongs to a set of admissible coefficients. It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence. Based on this result the existence of a quasisolution of the inverse problem is obtained in the appropriate class of admissible coefficients.