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Matematicheskie Zametki, 2015, Volume 98, Issue 3, Pages 448–462
DOI: https://doi.org/10.4213/mzm10464 (Mi mzm10464) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Global Unsolvability of One-Dimensional Problems for Burgers-Type Equations

E. V. Yushkov, M. O. Korpusov

Lomonosov Moscow State University
Full-text PDF (495 kB) Citations (6)
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DOI: https://doi.org/10.4213/mzm10464
Abstract: In this paper, we study the global solvability of well-known equations used to describe nonlinear processes with dissipation, namely, the Burgers equation, the Korteweg–de Vries–Burgers equation, and the modified Korteweg–de Vries–Burgers equation. Using a method due to Pokhozhaev, we obtain necessary conditions for the blow-up of global solutions and estimates of the blow-up time and blow-up rate in bounded and unbounded domains. We also study the effect of linear and nonlinear viscosity on the occurrence of a gradient catastrophe in finite time.
Keywords: Burgers equation, global unsolvability of Burgers-type equations, Korteweg–de Vries–Burgers equation, nonlinear process with dissipation, blow-up time, gradient catastrophe, maximum principle, method of test functions.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-12460-офи-м
This work was supported by the Russian Foundation for Basic Research under grant 13-01-12460-ofi-m.
Received: 24.02.2014
English version:
Mathematical Notes, 2015, Volume 98, Issue 3, Pages 503–514
DOI: https://doi.org/10.1134/S0001434615090163
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: E. V. Yushkov, M. O. Korpusov, “Global Unsolvability of One-Dimensional Problems for Burgers-Type Equations”, Mat. Zametki, 98:3 (2015), 448–462; Math. Notes, 98:3 (2015), 503–514
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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