Article
MSC:
34A55,
34G10,
34G25,
34G99,
35K65,
35R30,
47A55 | MR 3083520 | Zbl 06221237 | DOI: 10.1007/s10492-013-0019-1
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Keywords:
identification problem; perturbation theory for linear operators; degenerate differential equation
identification problem; perturbation theory for linear operators; degenerate differential equation
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.
References:
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