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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
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.
Received: 24.02.2014
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
Linking options:
https://www.mathnet.ru/eng/mzm10464https://doi.org/10.4213/mzm10464 https://www.mathnet.ru/eng/mzm/v98/i3/p448
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Abstract page: | 505 | Full-text PDF : | 207 | References: | 45 | First page: | 36 |
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