Autonomous Ovsyannikov theorem and applications to nonlocal evolution equations and systems
Autonomous Ovsyannikov theorem and applications to nonlocal evolution equations and systems
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DOI：
10.1016/j.jfa.2015.06.008
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发表时间：
2016
影响因子：
1.7
通讯作者：
Rafael F. Barostichi;A. Himonas;G. Petronilho
中科院分区：
文献类型：
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作者：
Rafael F. Barostichi;A. Himonas;G. Petronilho
这项工作提出了一个 Ovsyannikov 型定理，用于解决巴拿赫空间递减规模中的自治抽象柯西问题，除了解的存在性和唯一性之外，还提供了对解的分析寿命的估计。然后，利用该定理研究了圆和直线上的解析函数空间中具有初始数据的Camassa-Holm型方程和系统的柯西问题，这是本文的主要目标。最后，它研究了解析函数空间中数据到解决方案映射的连续性。
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.