This article is cited in 12 papers

Local solvability and solution blowup for the Benjamin–Bona–Mahony–Burgers equation with a nonlocal boundary condition

M. O. Korpusov, A. A. Panin

Lomonosov Moscow State University, Moscow, Russia

Abstract: We consider a model initial–boundary value problem for the Benjamin–Bona–Mahony–Burgers equation with initial conditions having a physical meaning. We prove the unique local solvability in the classical sense and obtain sufficient conditions for blowup and an estimate of the blowup time. To prove the blowup, we use the known test function method developed in papers by V. A. Galaktionov, E. L. Mitidieri, and S. I. Pohozaev. We note that this is one of the first results toward the blowup for the considered equation.

Keywords: blowup, local solvability, Benjamin–Bona–Mahony–Burgers equation.

Received: 27.09.2012

DOI: 10.4213/tmf8417

 English version: Theoretical and Mathematical Physics, 2013, 175:2, 580–591

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