Identification of Time and Space Dependent Relaxation Kernels for Materials with Memory Related to Cylindrical Domains, I*

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 VsV1=V2 , V1 and V2 being, respectively, an interval in R and a smooth enough domain in Rn. 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.