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Identification problems for degenerate parabolic equations. (English) Zbl 1289.35183

Summary: This paper deals with multivalued identification problems for parabolic equations. The problem consists of recovering a source term from the knowledge of an additional observation of the solution by exploiting some accessible measurements. Semigroup approach and perturbation theory for linear operators are used to treat the solvability in the strong sense of the problem. As an important application we derive the corresponding existence, uniqueness, and continuous dependence results for different degenerate identification problems. Applications to identification problems for the Stokes system, Poisson-heat equation, and Maxwell system are given to illustrate the theory.

MSC:

35K65 Degenerate parabolic equations
34G10 Linear differential equations in abstract spaces
34A55 Inverse problems involving ordinary differential equations
47A55 Perturbation theory of linear operators
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