This article is cited in 11 papers

Blowup of a positive-energy solution of model wave equations in nonlinear dynamics

M. O. Korpusov

M. V. Lomonosov Moscow State University

Abstract: We consider four problems of model nonlinear equations appearing in nonlinear mechanics and obtain sufficient conditions for the finite-time blowup of the problem solutions in bounded domains with homogeneous Dirichlet conditions. The initial system energy can be an arbitrarily large positive quantity. We use a modified Levin method to prove the blowup.

Keywords: finite-time blowup, generalized Klein–Gordon equation, nonlinear hyperbolic equation, nonlinear mixed boundary value problem, field theory.

Received: 18.06.2011

DOI: 10.4213/tmf6924

 English version: Theoretical and Mathematical Physics, 2012, 171:1, 421–434

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