Exponential Dichotomies for Elliptic Equations on Multidimensional Domains
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911539585351680 |
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| author | Beck, Margaret Goh, Ryan Haslam-Hyde, Alanna |
| author_facet | Beck, Margaret Goh, Ryan Haslam-Hyde, Alanna |
| contents | The existence of exponential dichotomies has been well-established as a powerful tool to study existence, stability, and bifurcations of coherent structures. Currently, the application of exponential dichotomies to elliptic problems posed on multi-dimensional domains is predominately limited to the context of cylindrical spatial domains. Recent work by Beck et. al. (2021) has shown how to extend the method of spatial dynamics, in which one views a spatial variable as a time-like evolutionary variable, to general multi-dimensional spatial domains. In this paper, we show that exponential dichotomies exist for a class of spatial dynamical systems arising in this more general setting, thus allowing for their use in future analyses of coherent structures. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_00917 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exponential Dichotomies for Elliptic Equations on Multidimensional Domains Beck, Margaret Goh, Ryan Haslam-Hyde, Alanna Analysis of PDEs Dynamical Systems 35A24, 34D09, 37L10, 35B36 The existence of exponential dichotomies has been well-established as a powerful tool to study existence, stability, and bifurcations of coherent structures. Currently, the application of exponential dichotomies to elliptic problems posed on multi-dimensional domains is predominately limited to the context of cylindrical spatial domains. Recent work by Beck et. al. (2021) has shown how to extend the method of spatial dynamics, in which one views a spatial variable as a time-like evolutionary variable, to general multi-dimensional spatial domains. In this paper, we show that exponential dichotomies exist for a class of spatial dynamical systems arising in this more general setting, thus allowing for their use in future analyses of coherent structures. |
| title | Exponential Dichotomies for Elliptic Equations on Multidimensional Domains |
| topic | Analysis of PDEs Dynamical Systems 35A24, 34D09, 37L10, 35B36 |
| url | https://arxiv.org/abs/2510.00917 |