The finite-time blowup of the solution of an initial boundary-value problem for the nonlinear equation of ion sound wavesстатья
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Аннотация: We obtain blowup conditions for the solutions of initial boundary-value problems for the nonlinear equation of ion sound waves in a hydrogen plasma in the approximation of “hot” electrons and “heavy” ions. A specific characteristic of this nonlinear equation is the noncoercive nonlinearity of the form ∂ t |∇u| 2
∂t|∇u|2
, which complicates its study by any energy method. We solve this problem by the Mitidieri–Pohozaev method of nonlinear capacity.