Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4589724 | Journal of Functional Analysis | 2016 | 29 Pages |
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Rafael F. Barostichi, A. Alexandrou Himonas, Gerson Petronilho,