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Asymptotic behaviour of solutions of hyperbolic conservation laws ut + (um)x = 0 as m → ∞ with inconsistent initial values

Published online by Cambridge University Press:  14 November 2011

Xiangsheng Xu
Xiangsheng Xu
Affiliation:
Department of Mathematics, Texas A& M University, College Station, TX 77843, U.S.A.
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Synopsis

We study the behaviour of solutions u = um of ut, + (um)x = 0 for t > 0, x ∊ R, u(x, 0) = u0(x), u0 ≧0, u0 ∊ L1(R) as m → ∞. This is a singular perturbation problem about m = ∞ if u0 > 1 on a set of positive measure. It is shown that the limit exists and satisfies the stationary equation

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 113 , Issue 1-2 , 1989 , pp. 61 - 71
Copyright
Copyright © Royal Society of Edinburgh 1989

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