|
ИСТИНА |
Войти в систему Регистрация |
ИСТИНА ИНХС РАН |
||
On the conditions for the breaking of oscillations in a cold plasmaстатья Электронная публикация
- Авторы: Rozanova Olga S., Chizhonkov Eugeniy V.
- Журнал: ArXiv e-prints
- Год издания: 2019
- Первая страница: 1912.08152
- DOI: 10.1007/s00033-020-01440-3
- Аннотация: The Cauchy problem for a quasilinear system of hyperbolic equationsdescribing plane one-dimensional relativistic oscillations of electrons in acold plasma is considered. For some simplified formulation of the problem, acriterion for the existence of a global in time solutions is obtained. For theoriginal problem, a sufficient condition for the loss of smoothness is found,as well as a sufficient condition for the solution to remain smooth at leastfor time $ 2 \pi $. In addition, it is shown that in the general case,arbitrarily small perturbations of the trivial state lead to the formation ofsingularities in a finite time. It is further proved that there are specialinitial data such that the respective solution remains smooth for all time,even in the relativistic case. Periodic in space traveling wave gives anexample of such a solution. In order for such a wave to be smooth, the velocityof the wave must be greater than a certain constant that depends on the initialdata. Nevertheless, arbitrary small perturbation of general form destroys theseglobal in time smooth solutions. The nature of the singularities of thesolutions is illustrated by numerical examples.
- Добавил в систему: Розанова Ольга Сергеевна