Abstract:
New high-order nonlinear equations of the Sobolev type describing ion-sound plasma waves in an external electric or magnetic field are derived. Despite the cumbersome form of the equations, research techniques are developed for corresponding initial and initial-boundary value problems. Specifically, based on the present results, sufficient conditions for blow-up formation will be proposed later.
Key words:nonlinear equations of Sobolev type, blow-up, local solvability, nonlinear capacity, blow-up time estimates.
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