Geodesic
Blow-up of ion acoustic waves in a plasma
Sbornik. Mathematics, Tome 202 (2011) no. 1, pp. 35-60

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A model equation is considered, which describes ion acoustic waves in a plasma taking account of strong nonlinear dissipation and nonlinear sources of general form. For the corresponding initial-boundary value problems in a bounded 3D-domain with zero Dirichlet condition at the boundary of the domain, necessary conditions for the blow-up of a solution are obtained. An estimate for the life time of the solution is also obtained. Finally, it is proved that for any initial data in $\mathbb H_0^1(\Omega)$ the problem under consideration has a local strong generalized solution (in time), that is, it is shown that a blow-up always takes nonzero time. Bibliography: 16 titles.
Keywords: finite-time blow-up, nonlinear Sobolev equations, nonlinear mixed boundary value problems, waves in a plasma. 
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     author = {M. O. Korpusov},
     title = {Blow-up of ion acoustic waves in a plasma},
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M. O. Korpusov. Blow-up of ion acoustic waves in a plasma. Sbornik. Mathematics, Tome 202 (2011) no. 1, pp. 35-60. http://geodesic.mathdoc.fr/item/SM_2011_202_1_a2/