The power series method for nonlocal and nonlinear evolution equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:443

Article

Barostichi, Rafael F.¹  Himonas, A. Alexandrou²  Petronilho, Gerson¹ 

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

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

关键词: Abstract Cauchy-Kovalevsky and Ovsyannikov theorems;    Nonlinear and nonlocal evolution equations;    Analytic spaces and lifespan;    Integrable equations;    Camassa-Holm type equations;    Peakon traveling wave solutions;   

DOI  :  10.1016/j.jmaa.2016.05.061

来源: Elsevier

【 摘 要 】

The initial value problem for a 4-parameter family of nonlocal and nonlinear evolution equations with data in a space of analytic functions is solved by using a power series method in abstract Banach spaces. In addition to determining the power series expansion of the solution, this method also provides an estimate of the analytic lifespan expressed in terms of the norm of the initial data, thus establishing an abstract Cauchy-Kovalevsky type theorem for these equations. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free