Inverse and direct problems for nonautonomous degenerate integrodifferential equations of parabolic type with Dirichlet boundary conditions

This paper deals with inverse and direct problems related to linear degenerate integrodifferential equations of parabolic type. The study of the direct problem is highly affected by the related inverse problems so that the results of the direct problems are just those needed to solve – locally in time – the inverse one. The latter is concerned with recovering – in a Hölder class – a memory kernel depending on time only.