## Differential and Integral Equations

### Sharp extensions for convoluted solutions of wave equations

#### 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