This article is cited in 4 papers

Blow-up of ion-sound waves in plasma with non-linear sources on the boundary

M. O. Korpusov

M. V. Lomonosov Moscow State University, Faculty of Physics

Abstract: We consider a model equation of ion-sound waves in ‘non-magnetized’ plasma taking account of non-linear sources localized on the boundary. This generates a non-linear dynamical boundary condition which is ‘close’ to the non-linear Neumann–Dirichlet condition. We prove the existence of a weak generalized solution of this initial-boundary value problem and obtain sufficient conditions for the blow-up of this solution in finite time. We give an upper bound for the time of existence of the solution, which equals its blow-up time. We also obtain sufficient conditions for the existence of a strong generalized solution.

Keywords: blow-up, Sobolev equations, plasma, ion-sound waves, non-linear boundary conditions.

UDC: 517.957

MSC: 35M13, 35B45, 76X05

Received: 13.01.2010

DOI: 10.4213/im4285

 English version: Izvestiya: Mathematics, 2012, 76:2, 310–345

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