This article is cited 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.

UDC: 517.9

Received: 24.02.2014

DOI: 10.4213/mzm10464

 English version: Mathematical Notes, 2015, 98:3, 503–514

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