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Blowup of solutions of a Korteweg-de Vries-type equation

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Abstract

We investigate the nonlinear third-order differential equation (uxx − u)t + u xxx + uux = 0 describing the processes in semiconductors with a strong spatial dispersion. We study the problem of the existence of global solutions and obtain sufficient conditions for the absence of global solutions for some initial boundary value problems corresponding to this equation. We consider examples of solution blowup for initial boundary value and Cauchy problems. We use the Mitidieri-Pokhozhaev nonlinear capacity method.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    E. V. Yushkov

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  1. E. V. Yushkov
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Correspondence to E. V. Yushkov.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 172, No. 1, pp. 64–71, July, 2012.

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Yushkov, E.V. Blowup of solutions of a Korteweg-de Vries-type equation. Theor Math Phys 172, 932–938 (2012). https://doi.org/10.1007/s11232-012-0087-5

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