Invariance Property of a Conservation Law without Convexity

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The main goal of this paper is to investigate the mechanism of a conservation law that gives the N-wave like asymptotics. It turns out that the positivity of the flux function provides a certain invariance of solution which singles out the right asymptotics among two parameter family of N-waves. Two kinds of long time asymptotic convergence orders in L(1)-norm to this N-wave are proved using a potential comparison technique. The first one is of the magnitude of the N-wave itself and the second one is of order 1/t. We observe that these asymptotic convergence orders are related to space and time translations of potentials.
Publisher
INDIANA UNIV MATH JOURNAL
Issue Date
2009
Language
English
Article Type
Article
Keywords

FAST-DIFFUSION-EQUATIONS; POROUS-MEDIUM EQUATION; ASYMPTOTIC-BEHAVIOR; NONLINEAR DIFFUSION; HYPERBOLIC SYSTEMS; SELF-SIMILARITY; N-WAVES; ENTROPY; RATES; DECAY

Citation

INDIANA UNIVERSITY MATHEMATICS JOURNAL, v.58, no.2, pp.733 - 750

ISSN
0022-2518
DOI
10.1512/iumj.2009.58.3495
URI
http://hdl.handle.net/10203/176594
Appears in Collection
MA-Journal Papers(저널논문)
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