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Rates of Convergence to Self-Similar Solutions of Burgers' Equation

Burgers’ Equation ut + cuux = νuxx is a nonlinear partial differential equation which arises in models of traffic and fluid flow. It is perhaps the simplest equation describing waves under the influence of diffusion. We consider the large time behavior of solutions with exponentially localized initial conditions, analyzing the rate of convergence to a known self similar single-hump solution. We use the Cole-Hopf Transformation to convert the problem into a heat equation problem with exponentially localized initial conditions. The solution to this problem converges to a Gaussian. We then find an optimal Gaussian approximation which is accurate to order t−2. Transforming back to Burgers’ Equation yields a solution accurate to order t−2.

Identiferoai:union.ndltd.org:CLAREMONT/oai:scholarship.claremont.edu:hmc_theses-1126
Date01 May 2000
CreatorsMiller, Joel
PublisherScholarship @ Claremont
Source SetsClaremont Colleges
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceHMC Senior Theses

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