Autonomous Ovsyannikov theorem and applications to nonlocal evolution equations and systems

Autor(es)

Barostichi, Rafael F. ^[1] ; Himonas, A. Alexandrou ^[2] ; Petronilho, Gerson ^[1]

Afiliação do(s) autor(es)

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

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

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF FUNCTIONAL ANALYSIS; v. 270, n. 1, p. 330-358, JAN 1 2016.
• Citações Web of Science: 13

Resumo

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. (C) 2015 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 12/03168-7 - Teoria geométrica de EDP e várias variáveis complexas
• Beneficiário: Jorge Guillermo Hounie
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 12/00678-4 - Boa postura de equações fracamente dispersivas em espaços de funções analíticas
• Beneficiário: RAFAEL FERNANDO BAROSTICHI
• Modalidade de apoio: Auxílio à Pesquisa - Regular