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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

On the well-posedness of higher order viscous Burgers' equations

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Author(s):
Carvajal, Xavier [1] ; Panthee, Mahendra [2]
Total Authors: 2
Affiliation:
[1] Univ Fed Rio de Janeiro, Inst Matemat, BR-21941972 Rio de Janeiro, RJ - Brazil
[2] Univ Estadual Campinas, IMECC, BR-13083859 Campinas, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Source: Journal of Mathematical Analysis and Applications; v. 417, n. 1, p. 1-22, SEP 1 2014.
Web of Science Citations: 1
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. (AU)

FAPESP's process: 12/20966-4 - Well-posedness of the Cauchy problem and stability theory for nonlinear dispersive equations
Grantee:Mahendra Prasad Panthee
Support Opportunities: Regular Research Grants
FAPESP's process: 12/23054-6 - Properties of solutions of some dispersive equations
Grantee:Marcia Assumpcao Guimaraes Scialom
Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil