Inverse Coefficient Problems for Nonlinear Parabolic Differential Equations

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

ACTA MATHEMATICA SINICA-ENGLISH SERIES, vol.24, pp.1617-1624, 2008 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 10
  • Publication Date: 2008
  • Doi Number: 10.1007/s10114-008-6384-0
  • Title of Journal : ACTA MATHEMATICA SINICA-ENGLISH SERIES
  • Page Numbers: pp.1617-1624

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.