Abstract

We show a strategy recently developed to prove global in time existence and uniqueness results for integrodifferential inverse problems. The models we discuss in this paper are:

which are: the strongly damped wave equation with memory, the heat equation with memory and a model in the theory of combustion with memory, respectively. Here f is a given nonlinear function and Ω is a bounded domain in ℝ³. We determine u and the convolution memory kernel h under suitable initial–boundary conditions and assuming to know an additional restriction on the state variable u, for example of type

where φ and g are given functions representing the type of device used to measure u.