Differential and Integral Equations
- Differential Integral Equations
- Volume 28, Number 3/4 (2015), 309-332.
Sharp extensions for convoluted solutions of wave equations
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.
Differential Integral Equations, Volume 28, Number 3/4 (2015), 309-332.
First available in Project Euclid: 4 February 2015
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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