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Weighted identities for solutions of generalized Korteweg-de Vries equations

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Abstract

Consider the Korteweg-de Vries equation u t + u xxx + uu x = 0 and its generalization u t + u xxx + f(u)x = 0. For the solutions of these equations, weighted identities (differential and integral) are obtained. These identities make it possible to establish the blow-up (in finite time) of the solutions of certain boundary-value problems.

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Authors and Affiliations

  1. Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

    S. I. Pokhozhaev

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  1. S. I. Pokhozhaev
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Correspondence to S. I. Pokhozhaev.

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Original Russian Text © S. I. Pokhozhaev, 2011, published in Matematicheskie Zametki, 2011, Vol. 89, No. 3, pp. 393–409.

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Pokhozhaev, S.I. Weighted identities for solutions of generalized Korteweg-de Vries equations. Math Notes 89, 382–396 (2011). https://doi.org/10.1134/S0001434611030102

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