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Identification of a diffusion coefficient in strongly degenerate parabolic equations with interior degeneracy. (English) Zbl 1325.35278
The authors study two identification problems for a parabolic equation with a second-order differential degenerate operator both for homogeneous Dirichlet boundary conditions and for homogeneous Dirichlet-Neumann boundary conditions. Both problems are treated as nonlinear optimization problems by approaching them as optimal control problems in coefficients. The solution to the equation is assumed to be known on the whole time period for the first problem and at the final moment for the second problem. The authors first prove the existence and uniqueness of solutions to the considered problems by a variational technique, and then, they prove the existence of a minimizer constructed as a limit of a minimizing sequence. In order to get a clear representation of the control, the authors introduce an approximating control problem by regularizing the state equation.

35R30 Inverse problems for PDEs
35K65 Degenerate parabolic equations
49N45 Inverse problems in optimal control
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