Unbounded perturbations of the generator domain | Zendy

Saïd Hadd | Zendy; Rosanna Manzo | Zendy; Abdelaziz Rhandi | Zendy

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Unbounded perturbations of the generator domain

Author(s) -

Saïd Hadd,

Rosanna Manzo,

Abdelaziz Rhandi

Publication year - 2014

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2015.35.703

Subject(s) - generator (circuit theory) , domain (mathematical analysis) , semigroup , operator (biology) , embedding , banach space , physics , boundary (topology) , combinatorics , linear operators , mathematical physics , discrete mathematics , pure mathematics , mathematical analysis , mathematics , quantum mechanics , computer science , artificial intelligence , power (physics) , biochemistry , chemistry , repressor , transcription factor , bounded function , gene

Let X, U and Z be Banach spaces such that Z in X (with continuous and dense embedding), L : Z ->X be a closed linear operator and consider closed linear operators G, M : Z -> U. Putting conditions on G and M we show that the operator A = L with domain D(A) ={z∈Z: Gz=Mz} generates a C0- semigroup on X. Moreover, we give a variation of constants formula for the solution of an inhomogeneous problem.\ud \udSeveral examples will be given, in particular heat equation with distributed unbounded delay at the boundary condition

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