Instantaneous Blow-Up of a Weak Solution of a Problem in Plasma Theory on the Half-Lineстатья
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Дата последнего поиска статьи во внешних источниках: 21 мая 2019 г.
Аннотация:We consider a problem with some boundary and initial conditions for an equation
arising in the theory of ion-sound waves in plasma. We prove that if the spatial (one-dimensional)
variable ranges on an interval, then this problem has a unique nonextendable classical solution
which in general exists only locally in time. If the spatial variable varies on the half-line, then,
for the problem in question, we obtain an upper bound for the lifespan of its weak solution
and find initial conditions for which there exist no solutions even locally in time (instantaneous
blow-up of the weak solution). A similar result is obtained for the classical solution.