Differential and Integral Equations

Sharp extensions for convoluted solutions of wave equations

Pedro J. Miana and Verónica Poblete

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Abstract

In this paper, we give sharp extensions of convoluted solutions of wave equations in abstract Banach spaces. The main technique is to use the algebraic structure, for convolution products $\ast$ and $\ast_c$, of these solutions which are defined by a version of the Duhamel's formula. We define algebra homomorphisms, for the convolution product $\ast_c$, from a certain set of test-functions and apply our results to concrete examples of abstract wave equations.

Article information

Source
Differential Integral Equations, Volume 28, Number 3/4 (2015), 309-332.

Dates
First available in Project Euclid: 4 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.die/1423055230

Mathematical Reviews number (MathSciNet)
MR3306565

Zentralblatt MATH identifier
1363.47131

Subjects
Primary: 47D62: Integrated semigroups 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 44A10: Laplace transform 44A35: Convolution

Citation

Miana, Pedro J.; Poblete, Verónica. Sharp extensions for convoluted solutions of wave equations. Differential Integral Equations 28 (2015), no. 3/4, 309--332. https://projecteuclid.org/euclid.die/1423055230


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