Well-posedness of Non-autonomous Evolutionary Inclusions

TL;DR

This paper proves the well-posedness and causality of a class of non-autonomous differential inclusions in Hilbert spaces, with applications to thermoplasticity and viscoplasticity equations with time-dependent coefficients.

Contribution

It establishes the maximal monotonicity of involved relations and addresses causality for solutions in non-autonomous differential inclusions.

Findings

Well-posedness of non-autonomous differential inclusions in Hilbert spaces.

Causality of the solution operator is demonstrated.

Applications to thermoplasticity and viscoplasticity equations with time-dependent coefficients.

Abstract

A class of non-autonomous differential inclusions in a Hilbert space setting is considered. The well-posedness for this class is shown by establishing the mappings involved as maximal monotone relations. Moreover, the causality of the so established solution operator is addressed. The results are exemplified by the equations of thermoplasticity with time dependent coefficients and by a non-autonomous version of the equations of viscoplasticity with internal variables.