Geodesic
The~finite-time blowup of the~solution of an~initial boundary-value
Teoretičeskaâ i matematičeskaâ fizika, Tome 187 (2016) no. 3, pp. 447-454

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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.
Keywords: nonlinear capacity, blowup. 
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     author = {M. O. Korpusov},
     title = {The~finite-time blowup of the~solution of an~initial boundary-value},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {447--454},
     publisher = {mathdoc},
     volume = {187},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_187_3_a3/}
}
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M. O. Korpusov. The~finite-time blowup of the~solution of an~initial boundary-value. Teoretičeskaâ i matematičeskaâ fizika, Tome 187 (2016) no. 3, pp. 447-454. http://geodesic.mathdoc.fr/item/TMF_2016_187_3_a3/