The One-Phase Bifurcation For The p-Laplacian
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2018
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| _version_ | 1866911761075011584 |
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| author | Ali, Alaa Haj Wang, Peiyong |
| author_facet | Ali, Alaa Haj Wang, Peiyong |
| contents | A bifurcation about the uniqueness of a solution of a singularly perturbed free boundary problem of phase transition associated with the p-Laplacian, subject to given boundary condition is proved in this paper. We show this phenomenon by proving the existence of a third solution through the Mountain Pass Lemma when the boundary data decreases below a threshold. In the second part, we prove the convergence of an evolution to stable solutions, and show the Mountain Pass solution is unstable in this sense. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1801_06221 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | The One-Phase Bifurcation For The p-Laplacian Ali, Alaa Haj Wang, Peiyong Analysis of PDEs 35J92, 35J25, 35J62, 35K92, 35K20, 35K59 A bifurcation about the uniqueness of a solution of a singularly perturbed free boundary problem of phase transition associated with the p-Laplacian, subject to given boundary condition is proved in this paper. We show this phenomenon by proving the existence of a third solution through the Mountain Pass Lemma when the boundary data decreases below a threshold. In the second part, we prove the convergence of an evolution to stable solutions, and show the Mountain Pass solution is unstable in this sense. |
| title | The One-Phase Bifurcation For The p-Laplacian |
| topic | Analysis of PDEs 35J92, 35J25, 35J62, 35K92, 35K20, 35K59 |
| url | https://arxiv.org/abs/1801.06221 |