Traveling Sharp Waves of Porous Media Equations in Spatially Periodic Environment
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915353986072576 |
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| author | Lou, Bendong |
| author_facet | Lou, Bendong |
| contents | We consider one dimensional porous media equations in spatially periodic environment. We will construct a periodic traveling sharp wave whose profile tends to a positive steady state at left infinity and takes zero on the right half line, with a free boundary satisfying the Darcy's law. Our method is to take the limit for a sequence of normalized solutions starting at Heaviside type of initial data. The crucial step is to give a uniform positive lower bound for the instantaneous speed of the free boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13269 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Traveling Sharp Waves of Porous Media Equations in Spatially Periodic Environment Lou, Bendong Analysis of PDEs 35K65, 35C07, 35K57, 35B10 We consider one dimensional porous media equations in spatially periodic environment. We will construct a periodic traveling sharp wave whose profile tends to a positive steady state at left infinity and takes zero on the right half line, with a free boundary satisfying the Darcy's law. Our method is to take the limit for a sequence of normalized solutions starting at Heaviside type of initial data. The crucial step is to give a uniform positive lower bound for the instantaneous speed of the free boundary. |
| title | Traveling Sharp Waves of Porous Media Equations in Spatially Periodic Environment |
| topic | Analysis of PDEs 35K65, 35C07, 35K57, 35B10 |
| url | https://arxiv.org/abs/2402.13269 |