This article is cited in 4 papers

Blowup in Korteweg–de Vries-type systems

E. V. Yushkov

Lomonosov Moscow State University, Moscow, Russia

Abstract: We consider a pair Korteweg–de Vries system of the Boussinesq type and its symmetric analogue. Such systems, which describe the behavior of a liquid in a channel, are shown to have no solutions defined globally in time under certain conditions. Using the method of nonlinear capacity, we obtain sufficient conditions for the solution blowup and estimate the blowup time for both these systems and for a generalized multicomponent Korteweg–de Vries-type system.

Keywords: Korteweg–de Vries-type system of equations, Boussinesq-type system, initial and boundary value problem, solvability global in time.

Received: 24.02.2012

DOI: 10.4213/tmf8331

 English version: Theoretical and Mathematical Physics, 2012, 173:2, 1498–1506

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