Evolution equations with nonlinear constitutive laws and memory effects

Abstract

Evolution equations are considered as operator equations involving a sum of the time-derivative operator $ \partial _{0} $ regarded as a normal operator in a suitable Hilbert space setting and another fairly arbitrary spatial operator $ A$ acting in a Hilbert space $ H $. As an extension of the linear theory the case of a class of nonlinear constitutive laws with memory effects is considered.