Geodesic
Blow-up of ion-sound waves in plasma with non-linear sources on the boundary
Izvestiya. Mathematics , Tome 76 (2012) no. 2, pp. 310-345

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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, plasma, ion-sound waves, non-linear boundary conditions.
Mots-clés : Sobolev equations 
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     author = {M. O. Korpusov},
     title = {Blow-up of ion-sound waves in plasma with non-linear sources on the boundary},
     journal = {Izvestiya. Mathematics },
     pages = {310--345},
     publisher = {mathdoc},
     volume = {76},
     number = {2},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2012_76_2_a3/}
}
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M. O. Korpusov. Blow-up of ion-sound waves in plasma with non-linear sources on the boundary. Izvestiya. Mathematics , Tome 76 (2012) no. 2, pp. 310-345. http://geodesic.mathdoc.fr/item/IM2_2012_76_2_a3/