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.
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Original Russian Text © M.O. Korpusov, S. Mikhailenko, 2017, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2017, Vol. 57, No. 7, pp. 1170–1175.
In memory of S.I. Pohozaev
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Korpusov, M.O., Mikhailenko, S. Instantaneous blow-up of classical solutions to the Cauchy problem for the Khokhlov–Zabolotskaya equation. Comput. Math. and Math. Phys. 57, 1167–1172 (2017). https://doi.org/10.1134/S0965542517030095
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DOI: https://doi.org/10.1134/S0965542517030095