Instantaneous blow up solutions for nonlinear Sobolev type equations on the Heisenberg Group
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916582168461312 |
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| author | Borikhanov, Meiirkhan B. Ruzhansky, Michael Torebek, Berikbol T. |
| author_facet | Borikhanov, Meiirkhan B. Ruzhansky, Michael Torebek, Berikbol T. |
| contents | In this paper, we study the nonlinear Sobolev type equations on the Heisenberg group. We show that the problems do not admit nontrivial local weak solutions, i.e. "instantaneous blow up" occurs, using the nonlinear capacity method. Namely, by choosing suitable test functions, we will prove an instantaneous blow up for any initial conditions $u_0,\,u_1\in L^q(\mathbb{H}^n)$ with $q\leq \frac{Q}{Q-2}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_05594 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Instantaneous blow up solutions for nonlinear Sobolev type equations on the Heisenberg Group Borikhanov, Meiirkhan B. Ruzhansky, Michael Torebek, Berikbol T. Analysis of PDEs In this paper, we study the nonlinear Sobolev type equations on the Heisenberg group. We show that the problems do not admit nontrivial local weak solutions, i.e. "instantaneous blow up" occurs, using the nonlinear capacity method. Namely, by choosing suitable test functions, we will prove an instantaneous blow up for any initial conditions $u_0,\,u_1\in L^q(\mathbb{H}^n)$ with $q\leq \frac{Q}{Q-2}$. |
| title | Instantaneous blow up solutions for nonlinear Sobolev type equations on the Heisenberg Group |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2303.05594 |