Logarithmic Sobolev Inequalities for Bounded Domains and Applications to Drift-Diffusion Equations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913246802345984 |
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| author | Abdo, Elie Lee, Fizay-Noah |
| author_facet | Abdo, Elie Lee, Fizay-Noah |
| contents | We prove logarithmic Sobolev inequalities on higher-dimensional bounded smooth domains based on novel Gagliardo-Nirenberg type interpolation inequalities. Moreover, we use them to address the long-time dynamics of some nonlinear nonlocal drift-diffusion models and prove the exponential decay of their solutions to constant steady states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18572 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Logarithmic Sobolev Inequalities for Bounded Domains and Applications to Drift-Diffusion Equations Abdo, Elie Lee, Fizay-Noah Analysis of PDEs Functional Analysis We prove logarithmic Sobolev inequalities on higher-dimensional bounded smooth domains based on novel Gagliardo-Nirenberg type interpolation inequalities. Moreover, we use them to address the long-time dynamics of some nonlinear nonlocal drift-diffusion models and prove the exponential decay of their solutions to constant steady states. |
| title | Logarithmic Sobolev Inequalities for Bounded Domains and Applications to Drift-Diffusion Equations |
| topic | Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2402.18572 |