Identification of time and space dependent relaxation kernels for materials with memory related to cylindrical domains. I (Q1378411)

The authors consider the problem of identifying a relaxation kernel for a first-order linear abstract integro-differential equation. Such a problem is related of the theory of stratified materials with memory in cylindrical domains \(\Omega= \Omega_1 \times \Omega_2\), \(\Omega_1\) and \(\Omega_2\) being, respectively, an interval in \(\mathbb{R}\) and a smooth enough domain in \(\mathbb{R}^n\). The relaxation kernel depends on time and one spatial variable. The proofs of the main results are given in part II [ibid. 213, No. 1, 63-90 (1997; reviewed below)].