Saved in:
Bibliographic Details
Main Authors: Aigner, Bernhard, Simsen, Jacson, Waurick, Marcus
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2605.19525
Tags: Add Tag
No Tags, Be the first to tag this record!
Table of Contents:
  • 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 Schrödinger-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.