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Solution blowup for systems of shallow-water equations

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Abstract

We consider initial-boundary value problems for systems of shallow-water equations. Using the testfunction method proposed by Pokhozhaev and Mitidieri, we study the effects of the boundary values and initial conditions on the occurrence, duration, and rate of blowup of the solutions of these problems. Under natural boundary conditions, we prove the existence of blowup in one- and two-dimensional problems in bounded and unbounded regions with dissipation and dispersion.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    M. O. Korpusov & E. V. Yushkov

Authors
  1. M. O. Korpusov
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  2. E. V. Yushkov
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Correspondence to M. O. Korpusov.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 175, No. 1, pp. 264–275, November, 2013.

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Korpusov, M.O., Yushkov, E.V. Solution blowup for systems of shallow-water equations. Theor Math Phys 177, 1505–1514 (2013). https://doi.org/10.1007/s11232-013-0119-9

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  • DOI: https://doi.org/10.1007/s11232-013-0119-9

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