Rates of Convergence to Self-Similar Solutions of Burgers' Equation
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 Lp 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 Lp error to the order of t−2+1/2p.
© 2003 Massachusetts Institute of Technology
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