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Exact thresholds in the dynamics of cold plasma with electron-ion collisionsстатья
- Авторы: Olga Rozanova, Eugeniy Chizhonkov, Maria Delova
- Журнал: ArXiv e-prints
- Год издания: 2020
- Первая страница: 2004.01226
- DOI: 10.1063/5.0033619
- Аннотация: We consider a quasilinear system of hyperbolic equations that describes plane one-dimensional non-relativistic oscillations of electrons in a cold plasma with allowance for electron-ion collisions. Accounting for collisions leads to the appearance of a term analogous to dry friction in a mechanical system, leading to a decrease in the total energy. We obtain a criterion for the existence of a global in time smooth solution to the Cauchy problem. It allows to accurately separate the initial data into two classes: one corresponds to a globally in time smooth solutions, and the other leads to a finite-time blowup. The influence of electron collision frequency ν on the solution is investigated. It is shown that there is a threshold value, after exceeding which the regime of damped oscillations is replaced by the regime of monotonic damping. The set of initial data corresponding to a globally in time smooth solution of the Cauchy problem expands with increasing ν, however, at an arbitrarily large value there are smooth initial data for which the solution forms a singularity in a finite time, and this time tends to zero as ν tends to infinity. The character of the emerging singularities is illustrated by numerical examples
- Добавил в систему: Розанова Ольга Сергеевна