Autonomous Ovsyannikov theorem and applications to nonlocal evolution equations and systems

Author(s)

Barostichi, Rafael F. ^[1] ; Himonas, A. Alexandrou ^[2] ; Petronilho, Gerson ^[1]

Affiliation

^[1] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP - Brazil

^[2] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 - USA

• Document type: Journal article
• Source: JOURNAL OF FUNCTIONAL ANALYSIS; v. 270, n. 1, p. 330-358, JAN 1 2016.
• Web of Science Citations: 13

Abstract

This work presents an Ovsyannikov type theorem for an autonomous abstract Cauchy problem in a scale of decreasing Banach spaces, which in addition to existence and uniqueness of solution provides an estimate about the analytic lifespan of the solution. Then, using this theorem it studies the Cauchy problem for Camassa-Holm type equations and systems with initial data in spaces of analytic functions on both the circle and the line, which is the main goal of this paper. Finally, it studies the continuity of the data-to-solution map in spaces of analytic functions. (C) 2015 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
• FAPESP's process: 12/00678-4 - Well-posedness of weakly dispersive equations in spaces of analytic functions
• Grantee: Rafael Fernando Barostichi
• Support Opportunities: Regular Research Grants