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TMF, 2012, Volume 170, Number 3, Pages 342–349 (Mi tmf6771)  

This article is cited in 4 scientific papers (total in 4 papers)

Blowup of solutions of the three-dimensional Rosenau–Burgers equation

M. O. Korpusov

Lomonosov Moscow State University, Moscow, Russia

Abstract: We consider the initial boundary value problem for the well-known three-dimensional Rosenau–Burgers equation in the cylinder $(0,L)\otimes\mathbb{S}$ (where $\mathbb{S}\subset\mathbb{R}^2$) for some boundary conditions. Using the test-function method, we obtain the result on the blowup of solutions of this initial boundary value problem during a finite time. This is one of the first results in the “blowup” direction for this equation.

Keywords: finite-time blowup, Sobolev-type nonlinear equation, nonlinear mixed boundary value problem, hydrodynamics, semiconductor, Rosenau–Burgers equation

DOI: https://doi.org/10.4213/tmf6771

Full text: PDF file (377 kB)
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English version:
Theoretical and Mathematical Physics, 2012, 170:3, 280–286

Bibliographic databases:

Received: 11.04.2011

Citation: M. O. Korpusov, “Blowup of solutions of the three-dimensional Rosenau–Burgers equation”, TMF, 170:3 (2012), 342–349; Theoret. and Math. Phys., 170:3 (2012), 280–286

Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf6771
  • http://mi.mathnet.ru/eng/tmf/v170/i3/p342

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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. A. A. Panin, “Local solvability and blowup of the solution of the Rosenau–Bürgers equation with different boundary conditions”, Theoret. and Math. Phys., 177:1 (2013), 1361–1376  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. Korpusov M.O., Yushkov E.V., “Local Solvability and Blow-Up For Benjamin-Bona-Mahony-Burgers, Rosenau-Burgers and Korteweg-de Vries-Benjamin-Bona-Mahony Equations”, Electron. J. Differ. Equ., 2014, 69  mathscinet  zmath  isi  elib
    3. A. A. Panin, “On Local Solvability and Blow-Up of Solutions of an Abstract Nonlinear Volterra Integral Equation”, Math. Notes, 97:6 (2015), 892–908  mathnet  crossref  crossref  mathscinet  isi  elib
    4. Tarasov V.E., “Partial fractional derivatives of Riesz type and nonlinear fractional differential equations”, Nonlinear Dyn., 86:3 (2016), 1745–1759  crossref  mathscinet  zmath  isi  elib  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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