Graduation Year
2000
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Andrew Bernoff
Reader 2
Jorge Aarao
Abstract
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.
Recommended Citation
Miller, Joel, "Rates of Convergence to Self-Similar Solutions of Burgers' Equation" (2000). HMC Senior Theses. 123.
https://scholarship.claremont.edu/hmc_theses/123
Thesis Proposal
