Nonautonomous systems of evolution inclusions
Abstract
We prove the existence of global solutions for some coupled systems of partially nonautonomous evolution inclusions comprised of a Cauchy problem with a compact resolvent semigroup generator and an evolution equation governed by a subdifferential of a real potential. Our system in particular includes nonautonomous generalized Schr\"odinger-Debye systems of inclusions with variable exponents, but extends to hyperbolic-parabolic systems of inclusions in particular to Maxwell-parabolic systems of inclusions. Methodologically, we extend an approach of Vrabie et al. to the nonautonomous case and make use of standard semigroup tools to accomodate non-parabolic behaviour of solutions paired with a new existence result for measurable selections. The combination of the latter two requires the set-valued coupling terms to be Hausdorff-continuous, to take bounded, convex and closed values, and to satisfy weak continuity with respect to one variable.
Cite
@article{arxiv.2605.19525,
title = {Nonautonomous systems of evolution inclusions},
author = {Bernhard Aigner and Jacson Simsen and Marcus Waurick},
journal= {arXiv preprint arXiv:2605.19525},
year = {2026}
}