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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2309.09499 |
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| _version_ | 1866910762789765120 |
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| author | Buchinger, Andreas Skrepek, Nathanael Waurick, Marcus |
| author_facet | Buchinger, Andreas Skrepek, Nathanael Waurick, Marcus |
| contents | Considering evolutionary equations in the sense of Picard, we identify a certain topology for material laws rendering the solution operator continuous if considered as a mapping from the material laws into the set of bounded linear operators, where the latter are endowed with the weak operator topology. The topology is a topology of vector-valued holomorphic functions and provides a lift of the previously introduced nonlocal $\mathrm{H}$-topology to particular holomorphic functions. The main area of applications are nonlocal homogenisation results for coupled systems of time-dependent partial differential equations. A continuous dependence result for a nonlocal model for cell migration is also provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_09499 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Weak Operator Continuity for Evolutionary Equations Buchinger, Andreas Skrepek, Nathanael Waurick, Marcus Analysis of PDEs Functional Analysis 32C18, 35B27, 74Q10, 78M40 Considering evolutionary equations in the sense of Picard, we identify a certain topology for material laws rendering the solution operator continuous if considered as a mapping from the material laws into the set of bounded linear operators, where the latter are endowed with the weak operator topology. The topology is a topology of vector-valued holomorphic functions and provides a lift of the previously introduced nonlocal $\mathrm{H}$-topology to particular holomorphic functions. The main area of applications are nonlocal homogenisation results for coupled systems of time-dependent partial differential equations. A continuous dependence result for a nonlocal model for cell migration is also provided. |
| title | Weak Operator Continuity for Evolutionary Equations |
| topic | Analysis of PDEs Functional Analysis 32C18, 35B27, 74Q10, 78M40 |
| url | https://arxiv.org/abs/2309.09499 |