Hypocoercivity for the non-linear semiconductor Boltzmann equation
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917840196468736 |
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| author | Pirner, Marlies Toshpulatov, Gayrat |
| author_facet | Pirner, Marlies Toshpulatov, Gayrat |
| contents | A kinetic model for semiconductor devices is considered on a flat torus. We prove exponential decay to equilibrium for this non-linear kinetic model by hypocoercivity estimates. This seems to be the first hypocoercivity result for this nonlinear kinetic equation for semiconductor devices without smallness assumptions. The analysis benefits from uniform bounds of the solution in terms of the equilibrium velocity distribution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11023 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hypocoercivity for the non-linear semiconductor Boltzmann equation Pirner, Marlies Toshpulatov, Gayrat Analysis of PDEs 35Q20, 35B40, 35Q81, 35Q82, 82C40 A kinetic model for semiconductor devices is considered on a flat torus. We prove exponential decay to equilibrium for this non-linear kinetic model by hypocoercivity estimates. This seems to be the first hypocoercivity result for this nonlinear kinetic equation for semiconductor devices without smallness assumptions. The analysis benefits from uniform bounds of the solution in terms of the equilibrium velocity distribution. |
| title | Hypocoercivity for the non-linear semiconductor Boltzmann equation |
| topic | Analysis of PDEs 35Q20, 35B40, 35Q81, 35Q82, 82C40 |
| url | https://arxiv.org/abs/2411.11023 |