Geodesic
Identification problems for degenerate parabolic equations
Applications of Mathematics, Tome 58 (2013) no. 4, pp. 389-404 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.1007/s10492-013-0019-1
Classification : 34A55, 34G10, 34G25, 34G99, 35K65, 35R30, 47A55
Keywords: identification problem; perturbation theory for linear operators; degenerate differential equation 
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     title = {Identification problems for degenerate parabolic equations},
     journal = {Applications of Mathematics},
     pages = {389--404},
     year = {2013},
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     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10492-013-0019-1/}
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Awawdeh, Fadi; Obiedat, Hamed M. Identification problems for degenerate parabolic equations. Applications of Mathematics, Tome 58 (2013) no. 4, pp. 389-404. doi: 10.1007/s10492-013-0019-1

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