Nonexistence of solutions to parabolic problems with a potential on weighted graphs
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916645448974336 |
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| author | Monticelli, Dario D. Punzo, Fabio Somaglia, Jacopo |
| author_facet | Monticelli, Dario D. Punzo, Fabio Somaglia, Jacopo |
| contents | We investigate nonexistence of nontrivial nonnegative solutions to a class of semilinear parabolic equations with a positive potential, posed on weighted graphs. Assuming an upper bound on the Laplacian of the distance and a suitable weighted space-time volume growth condition, we show that no global solutions exists. We also discuss the optimality of the hypotheses, thus recovering a critical exponent phenomenon of Fujita type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12058 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonexistence of solutions to parabolic problems with a potential on weighted graphs Monticelli, Dario D. Punzo, Fabio Somaglia, Jacopo Analysis of PDEs 35A01, 35A02, 35B44, 35K05, 35K58, 35R02 We investigate nonexistence of nontrivial nonnegative solutions to a class of semilinear parabolic equations with a positive potential, posed on weighted graphs. Assuming an upper bound on the Laplacian of the distance and a suitable weighted space-time volume growth condition, we show that no global solutions exists. We also discuss the optimality of the hypotheses, thus recovering a critical exponent phenomenon of Fujita type. |
| title | Nonexistence of solutions to parabolic problems with a potential on weighted graphs |
| topic | Analysis of PDEs 35A01, 35A02, 35B44, 35K05, 35K58, 35R02 |
| url | https://arxiv.org/abs/2404.12058 |