Dafermos Regularization of a Modified KdV-Burgers Equation

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Title: Dafermos Regularization of a Modified KdV-Burgers Equation
Author: Taylor, Monique Richardson
Advisors: Dr. Xiao-Biao Lin, Committee Member
Dr. Pierre Gremaud, Committee Member
Dr. Michael Shearer, Committee Member
Dr. Stephen Schecter, Committee Chair
Abstract: This project involves Dafermos regularization of a partial differential equation of order higher than 2. The modified Korteweg de Vries-Burgers equation is u_T + f(u)_X = alpha u_XX +beta u_XXX, where the flux is f(u) = u^3, alpha> 0, and beta is nonzero. We show the existence of Riemann-Dafermos solutions near a given Riemann solution composed of shock waves using geometric singular perturbation theory. When beta > 0, there is a possibility that the Riemann solution is composed of two shock waves as opposed to one. In addition, we use linearization to study the stability of the Riemann-Dafermos solutions.
Date: 2010-03-19
Degree: PhD
Discipline: Applied Mathematics
URI: http://www.lib.ncsu.edu/resolver/1840.16/4034

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