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.
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Project supported by NNSF of China Grant No. 10671211, Hu’nan Provincial NSF Grant No. 07JJ3005 and the Scientific and Technical Research Council (TUBITAK) of Turkey
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Ou, Y.H., Hasanov, A. & Liu, Z.H. Inverse coefficient problems for nonlinear parabolic differential equations. Acta. Math. Sin.-English Ser. 24, 1617–1624 (2008). https://doi.org/10.1007/s10114-008-6384-0
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DOI: https://doi.org/10.1007/s10114-008-6384-0