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Asymptotic properties of solutions of a KdV-Burgers equation with localized dissipation

We study the Korteweg-de Vries-Burgers equation. With a deep investigation into the spectral and smoothing properties of the linearized system, it is shown by applying Banach Contraction Principle and Gronwall's Inequality to the integral equation based on the variation of parameters formula and explicit representation of the operator semigroup associated with the linearized equation that, under appropriate assumption appropriate assumption on initial states w(x, 0), the nonlinear system is well-posed and its solutions decay exponentially to the mean value of the initial state in H1(O, 1) as t -> +". / Ph. D.

Identiferoai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/40133
Date24 October 2005
CreatorsHuang, Guowei
ContributorsMathematics, Russell, David L., Kim, Jong Uhn, Lin, Tao, Renardy, Michael J., Rogers, Robert C.
PublisherVirginia Tech
Source SetsVirginia Tech Theses and Dissertation
LanguageEnglish
Detected LanguageEnglish
TypeDissertation, Text
Formatv, 80 leaves, BTD, application/pdf, application/pdf
RightsIn Copyright, http://rightsstatements.org/vocab/InC/1.0/
RelationOCLC# 32777689, LD5655.V856_1994.H8357.pdf

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