An Oleinik-type estimate for a convection-diffusion equation and convergence to N-waves

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In this article we propose an Oleinik-type estimate for sign-changing solutions to a convection-diffusion equation u(t) + (\u\(gamma)/gamma)(x) = muu(xx), u(x,0) = u(0)(x), u,xepsilonR, 1<gammaless than or equal to2, u,t>0. Since the Oleinik entropy inequality holds for nonnegative solutions or inviscid case (mu = 0) only, the theoretical progress for the case was limited. In this paper we show that its solution satisfies an Oleinik-type estimate, t(2/gamma)u(x)less than or equal toC, 1<gammaless than or equal to2, t>0, where C = C(u(0), gamma) > 0. Using this estimate, the convergence to an N-wave is proved for sign changing solutions and the theoretical gap in asymptotic convergence of the corresponding problem is filled. (C) 2003 Elsevier Inc. All rights reserved.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2004-05
Language
English
Article Type
Article
Keywords

LARGE TIME BEHAVIOR; ASYMPTOTIC-BEHAVIOR; CONSERVATION-LAWS; BURGERS-EQUATION; REGULARITY

Citation

JOURNAL OF DIFFERENTIAL EQUATIONS, v.199, no.2, pp.269 - 289

ISSN
0022-0396
DOI
10.1016/j.jde.2003.10.014
URI
http://hdl.handle.net/10203/79239
Appears in Collection
MA-Journal Papers(저널논문)
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