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On the conditions for the breaking of oscillations in a cold plasmaстатья
Статья опубликована в высокорейтинговом журнале
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 10 февраля 2021 г.
- Авторы: Rozanova Olga S., Chizhonkov Eugeniy V.
- Журнал: Zeitschrift für angewandte Mathematik und Physik
- Том: 72
- Номер: 1
- Год издания: 2021
- Издательство: Birkhauser Verlag
- Местоположение издательства: Switzerland
- Номер статьи: 13
- DOI: 10.1007/s00033-020-01440-3
- Аннотация: The Cauchy problem for a quasilinear system of hyperbolic equations describing plane one-dimensional relativistic oscillations of electrons in a cold plasma is considered. For some simplified formulation of the problem, a criterion for the existence of a global in time solutions is obtained. For the original problem, a sufficient condition for blow-up is found, as well as a sufficient condition for the solution to remain smooth at least for time 2π. In addition, it is shown that in the general case, arbitrarily small perturbations of the trivial state lead to the formation of singularities in a finite time. It is further proved that there are special initial data such that the respective solution remains smooth for all time, even in the relativistic case. Periodic in space traveling wave gives an example of such a solution. In order for such a wave to be smooth, the velocity of the wave must be greater than a certain constant that depends on the initial data. Nevertheless, arbitrary small perturbation of general form destroys these global in time smooth solutions. The nature of the singularities of the solutions is illustrated by numerical examples.
- Добавил в систему: Розанова Ольга Сергеевна