A non-autonomous p-Adic diffusion equation on time changing graphs
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917738117595136 |
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| author | Bradley, Patrick Erik Ledezma, Ángel Morán |
| author_facet | Bradley, Patrick Erik Ledezma, Ángel Morán |
| contents | Motivated by the recently proven presence of ultrametricity in physical models (certain spin glasses) and the very recent study of Turing patterns on locally ultrametric state spaces, first non-autonomous diffusion operators on such spaces, where finitely many compact p-adic spaces are joined by a graph structure, are studied, including their Dirichlet and van Neumann eigenvalues. Secondly, the Cauchy problem for the heat equation associated with these operators is solved, its solution approximated by Trotter products, and thirdly, the corresponding Feller property as well as the Markov property (a Hunt process) is established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21555 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A non-autonomous p-Adic diffusion equation on time changing graphs Bradley, Patrick Erik Ledezma, Ángel Morán Analysis of PDEs Mathematical Physics Probability 35Q68 Motivated by the recently proven presence of ultrametricity in physical models (certain spin glasses) and the very recent study of Turing patterns on locally ultrametric state spaces, first non-autonomous diffusion operators on such spaces, where finitely many compact p-adic spaces are joined by a graph structure, are studied, including their Dirichlet and van Neumann eigenvalues. Secondly, the Cauchy problem for the heat equation associated with these operators is solved, its solution approximated by Trotter products, and thirdly, the corresponding Feller property as well as the Markov property (a Hunt process) is established. |
| title | A non-autonomous p-Adic diffusion equation on time changing graphs |
| topic | Analysis of PDEs Mathematical Physics Probability 35Q68 |
| url | https://arxiv.org/abs/2407.21555 |