Autonomous Ovsyannikov theorem and applications to nonlocal evolution equations and systems

作者：Barostichi Rafael F; Himonas A Alexandrou^*; Petronilho Gerson

来源：Journal of Functional Analysis, 2016, 270(1): 330-358.

DOI：10.1016/j.jfa.2015.06.008

• Ovsyannikov theorem for nonlocal equations
• Well-posedness of Cauchy problem in analytic spaces
• Integrable Camassa-Holm equations
• Continuity of solution map

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.

• 出版日期2016-1-1