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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2605.19525 |
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| _version_ | 1866910235864596480 |
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| author | Aigner, Bernhard Simsen, Jacson Waurick, Marcus |
| author_facet | Aigner, Bernhard Simsen, Jacson Waurick, Marcus |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19525 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nonautonomous systems of evolution inclusions Aigner, Bernhard Simsen, Jacson Waurick, Marcus Analysis of PDEs 35A01, 35A02 (Primary) 28B20, 26E25, 35Q35, 47H05, 47D06 (Secondary) 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. |
| title | Nonautonomous systems of evolution inclusions |
| topic | Analysis of PDEs 35A01, 35A02 (Primary) 28B20, 26E25, 35Q35, 47H05, 47D06 (Secondary) |
| url | https://arxiv.org/abs/2605.19525 |