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

Author(s)

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

• Document type: Journal article
• Source: Journal of Differential Equations; v. 263, n. 1, p. 732-764, JUL 5 2017.
• Web of Science Citations: 3

Abstract

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)

• FAPESP's process: 12/03168-7 - Geometric theory of PDE and several complex variables
• Grantee: Jorge Guillermo Hounie
• Support Opportunities: Research Projects - Thematic Grants