Identification of time and space dependent relaxation kernels for materials with memory related to cylindrical domains .1.

We consider the problem of identifying a relaxation kernel for a first-order linear abstract integrodifferential equation. Such a problem is related to the theory of stratified materials with memory in cylindrical domains Omega = Omega(1) X Omega(2), Omega(1) and Omega(2) being. respectively, an interval in R and a smooth enough domain in R-n. The relaxation kernel, in this case, depends on time and one spatial variable. The proofs of the main results will appear in a subsequent paper. (C) 1997 Academic Press.