We give a unified approach to a class of nonlinear parabolic inverse problems involving kernels of convolution type. Our main tools are optimal regularity results, in Sobolev and H¨older spaces, for parabolic equations and analytic semigroup theory. We apply the main abstract results (Theorems 2.1-2.2) to a model of population dynamics, to the theory of combustion of a material with memory and, finally, to a parabolic equation with elliptic part of order , which for = 1 is the heat equation with memory and with non-linearity containg derivatives up to order .
Cite this article
Fabio Colombo, D. Guidetti, A Unified Approach to Nonlinear Integro-Differential Inverse Problems of Parabolic Type. Z. Anal. Anwend. 21 (2002), no. 2, pp. 431–464DOI 10.4171/ZAA/1086