Asymptotic behavior of solutions to scalar conservation laws and optimal convergence orders to N-waves

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The goal of this article is to develop a new technique to obtain better asymptotic estimates for scalar conservation laws. General convex flux, f(n) (u) greater than or equal to 0, is considered with an assumption lim(u-->0) uf'(u)/f (u) = gamma > 1. We show that, under suitable conditions on the initial value, its solution converges to an N-wave in L-1 norm with the optimal convergence order of 0(1/t). The technique we use in this article is to enclose the solution with two rarefaction waves. We also show a uniform convergence order in the sense of graphs. A numerical example of this phenomenon is included. (C) 2003 Elsevier Science (USA). All rights reserved.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2003-07
Language
English
Article Type
Article
Keywords

LARGE TIME BEHAVIOR; BURGERS-EQUATION; SYSTEMS

Citation

JOURNAL OF DIFFERENTIAL EQUATIONS, v.192, no.1, pp.202 - 224

ISSN
0022-0396
DOI
10.1016/S0022-0396(03)00058-5
URI
http://hdl.handle.net/10203/79544
Appears in Collection
MA-Journal Papers(저널논문)
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