Geodesic
Global Unsolvability of One-Dimensional Problems for Burgers-Type Equations
Matematičeskie zametki, Tome 98 (2015) no. 3, pp. 448-462

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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, maximum principle, method of test functions.
Mots-clés : gradient catastrophe 
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     title = {Global {Unsolvability} of {One-Dimensional} {Problems} for {Burgers-Type} {Equations}},
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E. V. Yushkov; M. O. Korpusov. Global Unsolvability of One-Dimensional Problems for Burgers-Type Equations. Matematičeskie zametki, Tome 98 (2015) no. 3, pp. 448-462. http://geodesic.mathdoc.fr/item/MZM_2015_98_3_a12/