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Type: Artigo de periódico
Title: On The Supercritical Kdv Equation With Time-oscillating Nonlinearity
Author: Panthee M.
Scialom M.
Abstract: For the initial value problem (IVP) associated to the generalized Korteweg-de Vries (gKdV) equation with supercritical nonlinearity, numerical evidence [3] shows that, there are initial data φ ∈ H1(ℝ) such that the corresponding solution may blow-up in finite time. Also, with the evidence from numerical simulation [1, 18], it has been claimed that a periodic time dependent coefficient in the nonlinearity would disturb the blow-up solution, either accelerating or delaying it. In this work, we investigate the IVP associated to the gKdV equation ut + ∂x 3u+g(ωt)∂x(uk+1) = 0, where g is a periodic function and k ≥ 5 is an integer. We prove that, for given initial data φ ∈ H1(ℝ), as {pipe}ω{pipe;} → ∞, the solution uω converges to the solution U of the initial value problem associated to Ut+∂x 3U + m(g)∂x(Uk+1) =0, with the same initial data, where m(g) is the average of the periodic function g. Moreover, if the solution U is global and satisfies ∥U∥Lx 5Lt 10<∞, then we prove that the solution uω is also global provided {pipe}ω{pipe} is sufficiently large. © 2012 Springer Basel.
Rights: fechado
Identifier DOI: 10.1007/s00030-012-0204-z
Date Issue: 2013
Appears in Collections:Unicamp - Artigos e Outros Documentos

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