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Solution Blowup for Nonlinear Equations of the Khokhlov–Zabolotskaya Type

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Abstract

We consider several nonlinear evolution equations sharing a nonlinearity of the form ∂2u2/∂t2. 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.

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  1. Lomonosov Moscow State University, Moscow, Russia

    M. O. Korpusov

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  1. M. O. Korpusov
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Correspondence to M. O. Korpusov.

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Korpusov, M.O. Solution Blowup for Nonlinear Equations of the Khokhlov–Zabolotskaya Type. Theor Math Phys 194, 347–359 (2018). https://doi.org/10.1134/S0040577918030030

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  • DOI: https://doi.org/10.1134/S0040577918030030

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