The repulsive Euler-Poisson equations with variable doping profile
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909243857174528 |
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| author | Rozanova, Olga S. |
| author_facet | Rozanova, Olga S. |
| contents | We prove that arbitrary smooth perturbations of the zero equilibrium state of the repulsive pressureless Euler-Poisson equations, which describe the behavior of cold plasma, blow up for any non-constant doping profile already in one-dimensional space. Further, we study small perturbations of the equilibrium to determine which properties of the doping profile contribute to the blow-up. We also propose a numerical procedure that allows one to find the blow-up time for any initial data and present examples of such calculations for various doping profiles for standard initial data, corresponding to the laser pulse. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03542 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The repulsive Euler-Poisson equations with variable doping profile Rozanova, Olga S. Analysis of PDEs Mathematical Physics 35Q60 35B44 35B20 35L80 We prove that arbitrary smooth perturbations of the zero equilibrium state of the repulsive pressureless Euler-Poisson equations, which describe the behavior of cold plasma, blow up for any non-constant doping profile already in one-dimensional space. Further, we study small perturbations of the equilibrium to determine which properties of the doping profile contribute to the blow-up. We also propose a numerical procedure that allows one to find the blow-up time for any initial data and present examples of such calculations for various doping profiles for standard initial data, corresponding to the laser pulse. |
| title | The repulsive Euler-Poisson equations with variable doping profile |
| topic | Analysis of PDEs Mathematical Physics 35Q60 35B44 35B20 35L80 |
| url | https://arxiv.org/abs/2401.03542 |