Blow-up and global existence for semilinear parabolic equations on infinite graphs
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914860467486720 |
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| author | Grillo, Gabriele Meglioli, Giulia Punzo, Fabio |
| author_facet | Grillo, Gabriele Meglioli, Giulia Punzo, Fabio |
| contents | We investigate existence of global in time solutions and blow-up of solutions to the semilinear heat equation posed on infinite graphs. The source term is a general function $f(u)$. We always assume that the infimum of the spectrum of the Laplace operator $λ_1(G)$ on the graph is positive. According to an interaction between the behavior of $f$ close to $0$ and the value $λ_1(G)$, we get the existence of a global in time solution or blow-up of any nonnegative solution, provided that the initial datum is nontrivial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15069 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Blow-up and global existence for semilinear parabolic equations on infinite graphs Grillo, Gabriele Meglioli, Giulia Punzo, Fabio Analysis of PDEs We investigate existence of global in time solutions and blow-up of solutions to the semilinear heat equation posed on infinite graphs. The source term is a general function $f(u)$. We always assume that the infimum of the spectrum of the Laplace operator $λ_1(G)$ on the graph is positive. According to an interaction between the behavior of $f$ close to $0$ and the value $λ_1(G)$, we get the existence of a global in time solution or blow-up of any nonnegative solution, provided that the initial datum is nontrivial. |
| title | Blow-up and global existence for semilinear parabolic equations on infinite graphs |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.15069 |