Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 67, pp. 1-16.
Title: Recovering a time- and space-dependent kernel in a
hyperbolic integro-differential equation from a
restricted Dirichlet-to-Neumann Operator
Author: Jaan Janno (Tallinn Univ. of Technology, Estonia)
Abstract:
We prove that a space- and time-dependent kernel occurring in a hyperbolic
integro-differential equation in three space dimensions can be uniquely
reconstructed from the restriction of the Dirichlet-to-Neumann operator of
the equation into a set of Dirichlet data of the form of products of a
fixed time-dependent coefficient times arbitrary space-dependent functions.
Submitted March 29, 2004. Published May 3, 2004.
Math Subject Classifications: 35R30, 45K05, 74J25.
Key Words: Inverse problem; Dirichlet-to-Neumann operator;
hyperbolic equation; viscoelasticity.