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Inverse coefficient problems for nonlinear parabolic differential equations. (English) Zbl 1157.35402

Summary: 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.

MSC:

35K55 Nonlinear parabolic equations
49J20 Existence theories for optimal control problems involving partial differential equations
65K10 Numerical optimization and variational techniques
35R30 Inverse problems for PDEs
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