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Stability and Convergence of Approximate Solutions to the Moore-Gibson-Thompson Equation

Knapp, Jason
Format
Thesis/Dissertation; Online
Author
Knapp, Jason
Advisor
Lasiecka, Irena
Abstract
We study the formulation of two approximation schemes for the solutions of a particular partial differential equation, the Moore-Gibson-Thompson equation, arising in nonlinear acoustics. The established theory of well posedness for the linear and nonlinear equation is summarized, and then the main results of the work are the time-stability of the approximate solutions by either scheme, and the convergence of the approximations to the original solution with explicit rates of convergence provided.
Language
English
Published
University of Virginia, Department of Mathematics, PHD (Doctor of Philosophy), 2014
Published Date
2014-04-29
Degree
PHD (Doctor of Philosophy)
Collection
Libra ETD Repository
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