Semilinear wave inequalities with double damping and potential terms on Riemannian Manifolds
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914028021874688 |
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| author | Jleli, Mohamed Ruzhansky, Michael Samet, Bessem Torebek, Berikbol T. |
| author_facet | Jleli, Mohamed Ruzhansky, Michael Samet, Bessem Torebek, Berikbol T. |
| contents | We study a semilinear wave inequality with double damping on a complete noncompact Riemannian manifold. The considered problem involves a potential function $V$ depending on the space variable in front of the power nonlinearity and an inhomogeneous term $W$ depending on both time and space variables. Namely, we establish sufficient conditions for the nonexistence of weak solutions in both cases: $W\equiv 0$ and $W\not\equiv 0$. The obtained conditions depend on the parameters of the problem as well as the geometry of the manifold. Some special cases of manifolds, and of $V$ and $W$ are discussed in detail. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_00617 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Semilinear wave inequalities with double damping and potential terms on Riemannian Manifolds Jleli, Mohamed Ruzhansky, Michael Samet, Bessem Torebek, Berikbol T. Analysis of PDEs We study a semilinear wave inequality with double damping on a complete noncompact Riemannian manifold. The considered problem involves a potential function $V$ depending on the space variable in front of the power nonlinearity and an inhomogeneous term $W$ depending on both time and space variables. Namely, we establish sufficient conditions for the nonexistence of weak solutions in both cases: $W\equiv 0$ and $W\not\equiv 0$. The obtained conditions depend on the parameters of the problem as well as the geometry of the manifold. Some special cases of manifolds, and of $V$ and $W$ are discussed in detail. |
| title | Semilinear wave inequalities with double damping and potential terms on Riemannian Manifolds |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2312.00617 |