Abstract:
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 $\partial_t|\nabla u|^2$, which complicates its study by any energy method. We solve this problem by the Mitidieri–Pohozaev method of nonlinear capacity.
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