Diffusion limit of kinetic equations for multiple species charged particles
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2013
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866929464131190784 |
|---|---|
| author | Wu, Hao Lin, Tai-Chia Liu, Chun |
| author_facet | Wu, Hao Lin, Tai-Chia Liu, Chun |
| contents | In ionic solutions, there are multi-species charged particles (ions) with different properties like mass, charge etc. Macroscopic continuum models like the Poisson-Nernst-Planck (PNP) systems have been extensively used to describe the transport and distribution of ionic species in the solvent. Starting from the kinetic theory for the ion transport, we study a Vlasov-Poisson-Fokker-Planck (VPFP) system in a bounded domain with reflection boundary conditions for charge distributions and prove that the global renormalized solutions of the VPFP system converge to the global weak solutions of the PNP system, as the small parameter related to the scaled thermal velocity and mean free path tends to zero. Our results may justify the PNP system as a macroscopic model for the transport of multi-species ions in dilute solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1306_3053 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | Diffusion limit of kinetic equations for multiple species charged particles Wu, Hao Lin, Tai-Chia Liu, Chun Analysis of PDEs Mathematical Physics 35Q99, 35B25, 45K05, 35J05 In ionic solutions, there are multi-species charged particles (ions) with different properties like mass, charge etc. Macroscopic continuum models like the Poisson-Nernst-Planck (PNP) systems have been extensively used to describe the transport and distribution of ionic species in the solvent. Starting from the kinetic theory for the ion transport, we study a Vlasov-Poisson-Fokker-Planck (VPFP) system in a bounded domain with reflection boundary conditions for charge distributions and prove that the global renormalized solutions of the VPFP system converge to the global weak solutions of the PNP system, as the small parameter related to the scaled thermal velocity and mean free path tends to zero. Our results may justify the PNP system as a macroscopic model for the transport of multi-species ions in dilute solutions. |
| title | Diffusion limit of kinetic equations for multiple species charged particles |
| topic | Analysis of PDEs Mathematical Physics 35Q99, 35B25, 45K05, 35J05 |
| url | https://arxiv.org/abs/1306.3053 |