Open AccessIdentifying a BV-kernel in a hyperbolic integrodifferential equation
Author(s) -
Alfredo Lorenzi,
Eugenio Sinestrari
Publication year - 2008
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2008.21.1199
Subject(s) - uniqueness , bounded function , banach space , kernel (algebra) , mathematics , scalar (mathematics) , mathematical analysis , pure mathematics , hyperbolic partial differential equation , dirichlet boundary condition , boundary value problem , partial differential equation , geometry
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. 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 W1,1(0, T) used up to now to identify a. An application is given, in the framework of L2-spaces, to the case of hy- perbolic second-order integrodifferential equations endowed with initial and Dirichlet boundary conditions