Asymptotics of solutions to the porous medium equation near conical singularities
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917051674656768 |
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| author | Roidos, Nikolaos Schrohe, Elmar |
| author_facet | Roidos, Nikolaos Schrohe, Elmar |
| contents | We show that, on a manifold with conical singularities, the asymptotics of the solutions to the porous medium equation near the conical points are determined by the spectrum of the Laplacian on the cross-section of the cone. The key to this result is a precise description of the maximal domain of the cone Laplacian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_02044 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotics of solutions to the porous medium equation near conical singularities Roidos, Nikolaos Schrohe, Elmar Analysis of PDEs 35B40, 35C20, 58J40, 35K59, 35K65, 35R01 We show that, on a manifold with conical singularities, the asymptotics of the solutions to the porous medium equation near the conical points are determined by the spectrum of the Laplacian on the cross-section of the cone. The key to this result is a precise description of the maximal domain of the cone Laplacian. |
| title | Asymptotics of solutions to the porous medium equation near conical singularities |
| topic | Analysis of PDEs 35B40, 35C20, 58J40, 35K59, 35K65, 35R01 |
| url | https://arxiv.org/abs/2503.02044 |