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Identification problems for degenerate parabolic equations

Fadi Awawdeh, Hamed M. Obiedat (2013)

Applications of Mathematics

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...

Images of some functions and functional spaces under the Dunkl-Hermite semigroup

Néjib Ben Salem, Walid Nefzi (2013)

Commentationes Mathematicae Universitatis Carolinae

We propose the study of some questions related to the Dunkl-Hermite semigroup. Essentially, we characterize the images of the Dunkl-Hermite-Sobolev space, 𝒮 ( ) and L α p ( ) , 1 < p < , under the Dunkl-Hermite semigroup. Also, we consider the image of the space of tempered distributions and we give Paley-Wiener type theorems for the transforms given by the Dunkl-Hermite semigroup.

Implicit integral equations with discontinuous right-hand side

Filippo Cammaroto, Paolo Cubiotti (1997)

Commentationes Mathematicae Universitatis Carolinae

We consider the integral equation h ( u ( t ) ) = f ( I g ( t , x ) u ( x ) d x ) , with t [ 0 , 1 ] , and prove an existence theorem for bounded solutions where f is not assumed to be continuous.

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