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On the convolution operators arising in the study of abstract initial boundary value problems

Published online by Cambridge University Press:  14 November 2011

I. Alonso-Mallo
Affiliation:
Departamento de Matemática Aplicada y Computatión, Universidad de Valladolid, Vallodolid, Spain
C. Palencia
Affiliation:
Departamento de Matemática Aplicada y Computatión, Universidad de Valladolid, Vallodolid, Spain e-mail: palencia@cpd.uva.es

Extract

We consider convolution operators arising in the study of abstract initial boundary value problems. These operators are of the form

where {S(t)}t ≧0 is a C0-semigroup in a Banach space X,, with infinitesimal generator A0,: D(A0), ⊂ X, → X, and K(z): Y → X is a linxear, continuous mapping defined in another Banach space Y., We study the continuity of T between the spaces Lp([0, + ∞), Y), and Lq([0, + ∞), X), 1 ≦ p, q, ≦ + ∞. We give several examples of the applicability of the results to some familiar initial boundary value problems, including both parabolic and hyperbolic cases.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1996

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