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

Authors

Joel C. Miller '00, Harvey Mudd CollegeFollow
Andrew J. Bernoff, Harvey Mudd CollegeFollow

Student Co-author

HMC Undergraduate

Document Type

Article

Department

Mathematics (HMC)

Publication Date

2003

Abstract

We study the large-time behavior of solutions to Burgers' equation with localized initial conditions. Previous studies have demonstrated that these solutions converge to a self-similar asymptotic solution Θ(x, t) with an error whose L_p norm is of order t^−1+1/2p. Noting that the temporal and spatial translational invariance of the underlying equations leads to a two-parameter family of self-similar solutions Θ(x−x_*, t+t_*), we demonstrate that the optimal choice of x_* and t_* reduces the L_p error to the order of t^−2+1/2p.

Rights Information

© 2003 Massachusetts Institute of Technology

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

10.1111/1467-9590.t01-2-00226

Recommended Citation

Miller, J. C. and Bernoff, A. J. (2003), Rates of Convergence to Self-Similar Solutions of Burgers' Equation. Studies in Applied Mathematics, 111: 29–40. doi: 10.1111/1467-9590.t01-2-00226