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Theoretical and Mathematical Physics

, Volume 177, Issue 2, pp 1505–1514 | Cite as

Solution blowup for systems of shallow-water equations

  • M. O. KorpusovEmail author
  • E. V. Yushkov
Article

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.

Keywords

initial-boundary value problem finite-time blowup shallow water approximation 

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Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia

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