A note on asymptotics of linear dissipative kinetic equations in bounded domains
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912173093027840 |
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| author | Zhu, Yuzhe |
| author_facet | Zhu, Yuzhe |
| contents | We establish $L^2$-exponential decay properties for linear dissipative kinetic equations, including the time-relaxation and Fokker-Planck models, in bounded spatial domains with general boundary conditions that may not conserve mass. Their diffusion asymptotics in $L^2$ is also derived under general Maxwell boundary conditions. The proofs are simply based on energy estimates together with previous ideas from $L^2$-hypocoercivity and relative entropy methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_15758 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A note on asymptotics of linear dissipative kinetic equations in bounded domains Zhu, Yuzhe Analysis of PDEs We establish $L^2$-exponential decay properties for linear dissipative kinetic equations, including the time-relaxation and Fokker-Planck models, in bounded spatial domains with general boundary conditions that may not conserve mass. Their diffusion asymptotics in $L^2$ is also derived under general Maxwell boundary conditions. The proofs are simply based on energy estimates together with previous ideas from $L^2$-hypocoercivity and relative entropy methods. |
| title | A note on asymptotics of linear dissipative kinetic equations in bounded domains |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2309.15758 |