This article is cited in 7 papers

Blowup of solutions of the three-dimensional Rosenau–Burgers equation

M. O. Korpusov

Lomonosov Moscow State University, Moscow, Russia

Abstract: We consider the initial boundary value problem for the well-known three-dimensional Rosenau–Burgers equation in the cylinder $(0,L)\otimes\mathbb{S}$ (where $\mathbb{S}\subset\mathbb{R}^2$) for some boundary conditions. Using the test-function method, we obtain the result on the blowup of solutions of this initial boundary value problem during a finite time. This is one of the first results in the “blowup” direction for this equation.

Keywords: finite-time blowup, Sobolev-type nonlinear equation, nonlinear mixed boundary value problem, hydrodynamics, semiconductor, Rosenau–Burgers equation.

Received: 11.04.2011

DOI: 10.4213/tmf6771

 English version: Theoretical and Mathematical Physics, 2012, 170:3, 280–286

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