This article is cited in 6 papers

Instantaneous blow-up of classical solutions to the Cauchy problem for the Khokhlov–Zabolotskaya equation

M. O. Korpusov, S. G. Mikhailenko

Faculty of Physics, Moscow State University, Moscow, Russia

Abstract: The Cauchy problem for a second-order nonlinear equation with mixed derivatives is considered. It is proved that its classical local-in-time solution does not exist. The blow-up of the solution is proved by applying S. I. Pohozaev and E. L. Mitidieri's nonlinear capacity method.

Key words: nonlinear capacity, blow-up.

UDC: 519.634

Received: 28.10.2015

DOI: 10.7868/S0044466917030097

 English version: Computational Mathematics and Mathematical Physics, 2017, 57:7, 1167–1172

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