On integro-differential inclusions with operator-valued kernels

摘要

We study integro-differential inclusions in Hilbert spaces with operator-valued kernels and give sufficient conditions for the well-posedness. We show that several types of integro-differential equations and inclusions are covered by the class of evolutionary inclusions, and we therefore give criteria for the well-posedness within this framework. As an example, we apply our results to the equations of visco-elasticity and to a class of nonlinear integro-differential inclusions describing phase transition phenomena in materials with memory. Copyright (c) 2014 John Wiley & Sons, Ltd.