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.