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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...

Inhomogeneous linear differential equations in Banach spaces

Miroslav Sova (1978)

Časopis pro pěstování matematiky

Integrated semigroups and differential operators on LP spaces.

Matthias Hieber (1991)

Mathematische Annalen

Integrated semigroups and their application to complete second order Cauchy problems.

Frank Neubrander (1989)

Semigroup forum

Integrated semigroups of unbounded linear operators -- Cauchy problem. II.

Kravarušić, Ratko, Mijatović, Milorad, Pilipović, Stevan (1998)

Novi Sad Journal of Mathematics

Invariant measures for stochastic Cauchy problems with asymptotically unstable drift semigroup.

van Gaans, Onno, van Neerven, Jan (2006)

Electronic Communications in Probability [electronic only]

Isolated points of some sets of bounded cosine families, bounded semigroups, and bounded groups on a Banach space

Adam Bobrowski, Wojciech Chojnacki (2013)

Studia Mathematica

We show that if the set of all bounded strongly continuous cosine families on a Banach space X is treated as a metric space under the metric of the uniform convergence associated with the operator norm on the space 𝓛(X) of all bounded linear operators on X, then the isolated points of this set are precisely the scalar cosine families. By definition, a scalar cosine family is a cosine family whose members are all scalar multiples of the identity operator. We also show that if the sets of all bounded...