Life span of solutions to a semilinear parabolic equation on locally finite graphs
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916263527186432 |
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| author | Hu, Yuanyang Wang, Mingxin |
| author_facet | Hu, Yuanyang Wang, Mingxin |
| contents | Let $G=(V,E)$ be a locally finite connected graph. We develop the first eigenvalue method on $G$ introduced in 1963 by Kaplan \cite{Kaplan} on Euclidean space, the discrete Phragmén-Lindelöf principle of parabolic equations and upper and lower solutions method on $G$. Using these methods, we establish the estimates and asymptotic behaviour of the life span of solutions to a semilinear heat equation with initial data $λψ(x)$ for different scales of $λ$ on $G$ under some different conditions. Our results are different from the continuous case, which is related to the structure of the graph $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18173 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Life span of solutions to a semilinear parabolic equation on locally finite graphs Hu, Yuanyang Wang, Mingxin Analysis of PDEs Let $G=(V,E)$ be a locally finite connected graph. We develop the first eigenvalue method on $G$ introduced in 1963 by Kaplan \cite{Kaplan} on Euclidean space, the discrete Phragmén-Lindelöf principle of parabolic equations and upper and lower solutions method on $G$. Using these methods, we establish the estimates and asymptotic behaviour of the life span of solutions to a semilinear heat equation with initial data $λψ(x)$ for different scales of $λ$ on $G$ under some different conditions. Our results are different from the continuous case, which is related to the structure of the graph $G$. |
| title | Life span of solutions to a semilinear parabolic equation on locally finite graphs |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2405.18173 |