| Contents |
| 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
it provides an estimate about the analytic lifespan of the solution. Then it presents applications to
the Cauchy problem for Camassa-Holm type equations and systems with initial data in spaces of
analytic function on both the circle and the line. Finally, it studies the continuity of the data-to-solution map in spaces of analytic functions. |
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