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Teoreticheskaya i Matematicheskaya Fizika, 2013, Volume 177, Number 2, Pages 264–275
DOI: https://doi.org/10.4213/tmf8509 (Mi tmf8509) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Solution blowup for systems of shallow-water equations

M. O. Korpusov, E. V. Yushkov

Lomonosov Moscow State University, Moscow, Russia
Full-text PDF (358 kB) Citations (4)
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DOI: https://doi.org/10.4213/tmf8509
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.
Received: 02.02.2013
English version:
Theoretical and Mathematical Physics, 2013, Volume 177, Issue 2, Pages 1505–1514
DOI: https://doi.org/10.1007/s11232-013-0119-9
Bibliographic databases:
Document Type: Article
Language: Russian
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://www.mathnet.ru/eng/tmf8509
  • https://doi.org/10.4213/tmf8509
  • https://www.mathnet.ru/eng/tmf/v177/i2/p264
    • This publication is cited in the following 4 articles:
    1. Jleli M., Kirane M., Samet B., “Absence of Global Solutions For a Fractional in Time and Space Shallow-Water System”, Mathematics, 7:11 (2019), 1127  crossref  isi  scopus
    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  zmath  adsnasa  isi  elib
    4. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:106
    First page:41
     
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