Global analyticity for a generalized Camassa-Holm equation and decay of the radius of spatial analyticity

Autor(es)

Barostichi, Rafael F. ; Himonas, A. Alexandrou ; Petronilho, Gerson

• Tipo de documento: Artigo Científico
• Fonte: Journal of Differential Equations; v. 263, n. 1, p. 732-764, JUL 5 2017.
• Citações Web of Science: 3

Resumo

Global analytic solution in both the time and the space variables is proved for the Cauchy problem of a generalized CH equation, which contains as its members two integrable equations, namely the Camassa-Holm and the Novikov equations. The main assumptions are that the initial datum u(0)(x) is analytic on the line, it has uniform radius of analyticity r(0) > 0, and is such that the McKean quantity m(0)(x) = (1 - partial derivative(2)(x))u(0)(x) does not change sign. Furthermore, an explicit lower bound on the radius of space analyticity at later times is obtained, which is of the form L-3 exp(-L-1 exp(L-2t)), where L-1, L-2 and L-3 are appropriate positive constants. (C) 2017 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 12/03168-7 - Teoria geométrica de EDP e várias variáveis complexas
• Beneficiário: Jorge Guillermo Hounie
• Modalidade de apoio: Auxílio à Pesquisa - Temático