Well-posedness and orbital stability of periodic traveling waves for Schamel's equation
type: Item
instance of: scholarly article
title: Well-posedness and orbital stability of periodic traveling waves for Schamel's equation
zbMATH Open document ID: 1391.76078
DOI: 10.4171/ZAA/1611
author: Eleomar jun. Cardoso
author: Fábio Natali
author: Ademir Pastor
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2018-04-27T00:00:00Z
review text: Summary: In this paper we will prove results of global well-posedness and orbital stability of periodic traveling-wave solutions related to the Schamel equation. The global solvability will be established by using compactness tools. In order to overcome the lack of smoothness of the nonlinearity, we approximate the original problem by regularizing the nonlinear term through a convenient polynomial near the origin. By following an adaptation of the well-known method introduced by Grillakis, Shatah, and Strauss, the orbital stability will be determined by proving, under certain conditions, that the periodic waves minimize an augmented Hamiltonian.
Mathematics Subject Classification ID: 76B25
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 35Q51
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 6865178
zbMATH Keywords: Schamel's equation
zbMATH Keywords: well-posedness
zbMATH Keywords: periodic traveling waves
zbMATH Keywords: orbital stability
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/zaa/1611
OpenAlex ID: W2795156759
description: scientific article; zbMATH DE number 6865178