Comparison between model equations for long waves and blow-up phenomena

Autor(es)

Carvajal, X. ^[1] ; Panthee, M. ^[2] ; Scialom, M. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Fed Rio de Janeiro, Inst Matemat, Ave Athos da Silveira Ramos 149, POB 68530, BR-21945970 Rio de Janeiro, RJ - Brazil

^[2] Univ Estadual Campinas, Dept Matemat, Rua Sergio Buargue Holanda 651, BR-13083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Analysis and Applications; v. 442, n. 1, p. 273-290, OCT 1 2016.
• Citações Web of Science: 2

Resumo

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. (AU)

• Processo FAPESP: 12/20966-4 - Boa-colocação de problema de Cauchy e teoria de estabilidade para equações dispersivas não lineares
• Beneficiário: Mahendra Prasad Panthee
• Linha de fomento: Auxílio à Pesquisa - Regular
• Processo FAPESP: 12/23054-6 - Propriedades das soluções de algumas equações do tipo dispersivo
• Beneficiário: Marcia Assumpcao Guimaraes Scialom
• Linha de fomento: Auxílio à Pesquisa - Pesquisador Visitante - Brasil