Title page for ETD etd-10242005-124128


Type of Document Dissertation
Author Huang, Guowei
URN etd-10242005-124128
Title Asymptotic properties of solutions of a KdV-Burgers equation with localized dissipation
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Russell, David L. Committee Chair
Kim, Jong Uhn Committee Member
Lin, Tao Committee Member
Renardy, Michael J. Committee Member
Rogers, Robert C. Committee Member
Keywords
  • Korteweg-de Vries equation
  • Burgers equation
Date of Defense 1994-12-05
Availability restricted
Abstract

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 -> +∞.

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