Nonexistence of Solutions to classes of parabolic inequalities in the Riemannian setting
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914165161984000 |
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| author | von Criegern, Dorothea-Enrica Grillo, Gabriele Monticelli, Dario |
| author_facet | von Criegern, Dorothea-Enrica Grillo, Gabriele Monticelli, Dario |
| contents | We establish conditions for nonexistence of global solutions for a class of quasilinear parabolic problems with a potential on complete, non-compact Riemannian manifolds, including the Porous Medium Equation and the p-Laplacian with a potential term. Our results reveal the interplay between the manifold's geometry, the power nonlinearity, and the potential's behavior at infinity. Using a test function argument, we identify explicit parameter ranges where nonexistence holds. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_00203 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonexistence of Solutions to classes of parabolic inequalities in the Riemannian setting von Criegern, Dorothea-Enrica Grillo, Gabriele Monticelli, Dario Analysis of PDEs Differential Geometry 35K67, 35K59, 58J35, 35A01 We establish conditions for nonexistence of global solutions for a class of quasilinear parabolic problems with a potential on complete, non-compact Riemannian manifolds, including the Porous Medium Equation and the p-Laplacian with a potential term. Our results reveal the interplay between the manifold's geometry, the power nonlinearity, and the potential's behavior at infinity. Using a test function argument, we identify explicit parameter ranges where nonexistence holds. |
| title | Nonexistence of Solutions to classes of parabolic inequalities in the Riemannian setting |
| topic | Analysis of PDEs Differential Geometry 35K67, 35K59, 58J35, 35A01 |
| url | https://arxiv.org/abs/2505.00203 |