Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/81724
Type: Artigo
Title: On the well-posedness of higher order viscous Burgers' equations
Author: Carvajal, X.
Panthee, M.
Abstract: We consider higher order viscous Burgers' equations with generalized nonlinearity and study the associated initial value problems for given data in the L-2-based Sobolev spaces. We introduce appropriate time weighted spaces to derive multilinear estimates and use them in the contraction mapping principle argument to prove local well-posedness for data with Sobolev regularity below L-2. We also prove ill-posedness for this type of models and show that the local well-posedness results are sharp in some particular cases viz., when the orders of dissipation p, and nonlinearity k + 1, satisfy a relation p = 2k + 1. (C) 2014 Elsevier Inc. All rights reserved.
We consider higher order viscous Burgers' equations with generalized nonlinearity and study the associated initial value problems for given data in the L-2-based Sobolev spaces. We introduce appropriate time weighted spaces to derive multilinear estimates and use them in the contraction mapping principle argument to prove local well-posedness for data with Sobolev regularity below L-2. We also prove ill-posedness for this type of models and show that the local well-posedness results are sharp in some particular cases viz., when the orders of dissipation p, and nonlinearity k + 1, satisfy a relation p = 2k + 1.
Subject: Equações dispersivas
Korteweg-de Vries, Equação de
Boa-colocação local
Problemas de valor inicial
Country: Estados Unidos
Editor: Elsevier
Citation: Journal Of Mathematical Analysis And Applications. Academic Press Inc Elsevier Science, v. 417, n. 1, n. 1, n. 22, 2014.
Rights: fechado
Identifier DOI: 10.1016/j.jmaa.2014.02.056
Address: https://www.sciencedirect.com/science/article/pii/S0022247X14001942
Date Issue: 2014
Appears in Collections:IMECC - Artigos e Outros Documentos

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