Potential comparison and asymptotics in scalar conservation laws without convexity

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Two kinds of optimal convergence orders in L-1-norm to a self-similar solution are proved or conjectured for various evolutionary problems so far. The first convergence order is of the magnitude of the similarity solution itself and the second one is of order 1/t. Employing a potential comparison technique to scalar conservation laws we may easily see that these asymptotic convergence orders are related to space and time translation of potentials. We present the technique clearly in the simple setting of scalar conservation laws in one space dimension. (C) 2006 Published by Elsevier Inc.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2008-01
Language
English
Article Type
Article
Keywords

FAST-DIFFUSION-EQUATIONS; NONLINEAR DIFFUSION; SELF-SIMILARITY; N-WAVES; BEHAVIOR; ENTROPY

Citation

JOURNAL OF DIFFERENTIAL EQUATIONS, v.244, no.1, pp.40 - 51

ISSN
0022-0396
DOI
10.1016/j.jde.2006.08.013
URI
http://hdl.handle.net/10203/90911
Appears in Collection
MA-Journal Papers(저널논문)
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