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Type: Artigo de Periódico
Title: Comparison Between Model Equations For Long Waves And Blow-up Phenomena
Author: Carvajal
X; Panthee
M; Scialom
Abstract: Recently, to describe the unidirectional propagation of water waves, Bona et al. [7] introduced a fifth order KdV-BBM type model eta(t) + eta(x) - 1/6 eta(xxt) + delta(1)eta(xxxxt) + delta(2)eta(xxxxx) + 3/4(eta(2))(x) +gamma(eta(2))(xxx) - 1/12(eta(2)(x))(x) - 1/4(eta(3))(x) = 0, (0.1) where eta = eta(x, t) is a real-valued function, and delta(1) > 0, delta(2), gamma is an element of R. In this work, we plan to compare solution of the initial value problem (IVP) associated to the fifth-order KDV-BBM type model (0.1) to that of the IVP associated to the fifth-order KdV model u(t) + delta(3)u(xxxxx) + c(1)u(x)u(xx) + c(2)uu(xxx) + c(3)u(2)u(x) = 0, (0.2) where u = u(x, t) is a real-valued function and delta(3), c(1), c(2) and c(3) are real constants with delta(3) not equal 0. This later model (0.2) was proposed by Benney in [4] to describe the interaction of long and short waves. Also, we will study the possibility of blow-up phenomenon of the fifth-order KDV-BBM type model under certain restrictions on the coefficients. (C) 2016 Elsevier Inc. All rights reserved.
Subject: Nonlinear Dispersive Wave Equations
Water Wave Models
Kdv Equation
Bbm Equation
Cauchy Problem
Local & Global Well-posedness
Rights: fechado
Identifier DOI: 10.1016/j.jmaa.2016.04.062
Date Issue: 2016
Appears in Collections:Unicamp - Artigos e Outros Documentos

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