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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  and
C. Palencia
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
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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
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 3 , 1996 , pp. 515 - 539
Copyright
Copyright © Royal Society of Edinburgh 1996

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