Evolution Integro-Differential Inclusions

The aim of the present paper is to state and discuss the well-posedness of a new evolution inclusion governed by the subdifferential of a function \(\varphi \) perturbed both by a Carathéodory mapping and by an integral forcing term. The integrand of the forcing term depends on two time-variables. We prove the existence and uniqueness of local and global solution, assuming that \(\varphi \) is primal lower regular and the perturbation terms satisfy some standard conditions. The results are applied to the study of non-regular electrical circuits with tranmission line, Zener diode and inductor. A second application is concerned with semilinear heat equation with memory. These applications illustrate an additional novelty of our paper.