Geodesic
Solution blowup for nonlinear equations of the Khokhlov–Zabolotskaya type
Teoretičeskaâ i matematičeskaâ fizika, Tome 194 (2018) no. 3, pp. 403-417 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider several nonlinear evolution equations sharing a nonlinearity of the form $\partial^2\!u^2/\partial t^2$. Such a nonlinearity is present in the Khokhlov–Zabolotskaya equation, in other equations in the theory of nonlinear waves in a fluid, and also in equations in the theory of electromagnetic waves and ion–sound waves in a plasma. We consider sufficient conditions for a blowup regime to arise and find initial functions for which a solution understood in the classical sense is totally absent, even locally in time, i.e., we study the problem of an instantaneous blowup of classical solutions.
Keywords: finite-time blowup, nonlinear wave, instantaneous blowup. 
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M. O. Korpusov. Solution blowup for nonlinear equations of the Khokhlov–Zabolotskaya type. Teoretičeskaâ i matematičeskaâ fizika, Tome 194 (2018) no. 3, pp. 403-417. http://geodesic.mathdoc.fr/item/TMF_2018_194_3_a2/

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