Identifying a BV-kernel in a hyperbolic integrodifferential equation

Abstract

This paper is devoted to determining the scalar relaxation kernel $a$ in a second-order (in time) integrodifferential equation related to a Banach space when an additional measurement involving the state function is available. A result concerning global existence and uniqueness is proved. <br> The novelty of this paper consists in looking for the kernel $a$ in the Banach space $BV(0,T)$, consisting of functions of bounded variations, instead of the space $W^{1,1}(0,T)$ used up to now to identify $a$. <br> An application is given, in the framework of $L^2$-spaces, to the case of hyperbolic second-order integrodifferential equations endowed with initial and Dirichlet boundary conditions.