Abstract:
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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