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TMF, 2013, Volume 177, Number 2, Pages 264–275 (Mi tmf8509)  

This article is cited in 3 scientific papers (total in 3 papers)

Solution blowup for systems of shallow-water equations

M. O. Korpusov, E. V. Yushkov

Lomonosov Moscow State University, Moscow, Russia

Abstract: We consider initial-boundary value problems for systems of shallow-water equations. Using the test-function 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

DOI: https://doi.org/10.4213/tmf8509

Full text: PDF file (358 kB)
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English version:
Theoretical and Mathematical Physics, 2013, 177:2, 1505–1514

Bibliographic databases:

Received: 02.02.2013

Citation: M. O. Korpusov, E. V. Yushkov, “Solution blowup for systems of shallow-water equations”, TMF, 177:2 (2013), 264–275; Theoret. and Math. Phys., 177:2 (2013), 1505–1514

Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf8509
  • http://mi.mathnet.ru/eng/tmf/v177/i2/p264

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. V. Yushkov, M. O. Korpusov, “Global Unsolvability of One-Dimensional Problems for Burgers-Type Equations”, Math. Notes, 98:3 (2015), 503–514  mathnet  crossref  crossref  mathscinet  isi  elib
    2. M. O. Korpusov, E. V. Yushkov, “Global unsolvability of a nonlinear conductor model in the quasistationary approximation”, Theoret. and Math. Phys., 191:1 (2017), 471–479  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. E. V. Yushkov, M. O. Korpusov, “Gradient blow-up in generalized Burgers and Boussinesq equations”, Izv. Math., 81:6 (2017), 1286–1296  mathnet  crossref  crossref  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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