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Izv. RAN. Ser. Mat., 2012, Volume 76, Issue 2, Pages 103–140 (Mi izv4285)  

This article is cited in 1 scientific paper (total in 1 paper)

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.

DOI: https://doi.org/10.4213/im4285

Full text: PDF file (696 kB)
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English version:
Izvestiya: Mathematics, 2012, 76:2, 310–345

Bibliographic databases:

UDC: 517.957
MSC: 35M13, 35B45, 76X05
Received: 13.01.2010

Citation: M. O. Korpusov, “Blow-up of ion-sound waves in plasma with non-linear sources on the boundary”, Izv. RAN. Ser. Mat., 76:2 (2012), 103–140; Izv. Math., 76:2 (2012), 310–345

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. Zhang H., Zhang W., Hu Q., “Global Existence and Blow-Up of Solution For the Semilinear Wave Equation With Interior and Boundary Source Terms”, Bound. Value Probl., 2019, 18  crossref  mathscinet  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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