Global Unsolvability of One-Dimensional Problems for Burgers-Type Equationsстатья
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Дата последнего поиска статьи во внешних источниках: 22 ноября 2015 г.
Аннотация: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.