Nonautonomous systems of evolution inclusions

Bernhard Aigner; Jacson Simsen; Marcus Waurick

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arXiv · 2605.19525

Nonautonomous systems of evolution inclusions

Bernhard Aigner·Jacson Simsen·Marcus Waurick

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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.

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Bernhard Aigner, Jacson Simsen, Marcus Waurick. 2026-05-19. Nonautonomous systems of evolution inclusions. https://arxiv.org/abs/2605.19525

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