Gradient Flow Solutions For Porous Medium Equations with Nonlocal Lévy-type Pressure
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910858782703616 |
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| author | Foghem, Guy Padilla-Garza, David Schmidtchen, Markus |
| author_facet | Foghem, Guy Padilla-Garza, David Schmidtchen, Markus |
| contents | We study a porous medium-type equation whose pressure is given by a nonlocal Lévy operator associated to a symmetric jump Lévy kernel. The class of nonlocal operators under consideration appears as a generalization of the classical fractional Laplace operator. For the class of Lévy-operators, we construct weak solutions using a variational minimizing movement scheme. The lack of interpolation techniques is ensued by technical challenges that render our setting more challenging than the one known for fractional operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_15340 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Gradient Flow Solutions For Porous Medium Equations with Nonlocal Lévy-type Pressure Foghem, Guy Padilla-Garza, David Schmidtchen, Markus Analysis of PDEs 35A15, 35R09, 35R11, 46E35, 47A07, 49J40, 35S10 We study a porous medium-type equation whose pressure is given by a nonlocal Lévy operator associated to a symmetric jump Lévy kernel. The class of nonlocal operators under consideration appears as a generalization of the classical fractional Laplace operator. For the class of Lévy-operators, we construct weak solutions using a variational minimizing movement scheme. The lack of interpolation techniques is ensued by technical challenges that render our setting more challenging than the one known for fractional operators. |
| title | Gradient Flow Solutions For Porous Medium Equations with Nonlocal Lévy-type Pressure |
| topic | Analysis of PDEs 35A15, 35R09, 35R11, 46E35, 47A07, 49J40, 35S10 |
| url | https://arxiv.org/abs/2311.15340 |