Asymptotic agreement of moments and higher order contraction in the Burgers equation

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The purpose of this paper is to investigate the relation between the moments and the asymptotic behavior of solutions to the Burgers equation. The Burgers equation is a special nonlinear problem that turns into a linear one after the Cole-Hopf transformation. Our asymptotic analysis depends on this transformation. In this paper an asymptotic approximate solution is constructed, which is given by the inverse Cole-Hopf transformation of a summation of n heat kernels. The k-th order moments of the exact and the approximate solution are contracting with order O((root t)(k-2n-1+1/p)) in L(p)-norm as t -> infinity. This asymptotics indicates that the convergence order is increased by a similarity scale whenever the order of controlled moments is increased by one. The theoretical asymptotic convergence orders are tested numerically. (C) 2010 Elsevier Inc. All rights reserved.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2010-05
Language
English
Article Type
Article
Keywords

DIFFUSION EQUATION; CONSERVATION-LAWS; TIME BEHAVIOR; CONVERGENCE; WAVES; RATES

Citation

JOURNAL OF DIFFERENTIAL EQUATIONS, v.248, no.10, pp.2417 - 2434

ISSN
0022-0396
DOI
10.1016/j.jde.2010.01.006
URI
http://hdl.handle.net/10203/98409
Appears in Collection
MA-Journal Papers(저널논문)
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