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

Student Co-author

HMC Undergraduate

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Mathematics (HMC)

Publication Date



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(xx*, t+t*), we demonstrate that the optimal choice of x* and t* reduces the Lp error to the order of t−2+1/2p.

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© 2003 Massachusetts Institute of Technology

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