2000 Stability of $L^\infty$ solutions of Temple class systems
Alberto Bressan, Paola Goatin
Differential Integral Equations 13(10-12): 1503-1528 (2000). DOI: 10.57262/die/1356061137

Abstract

Let $u_t+f(u)_x=0$ be a strictly hyperbolic, genuinely nonlinear system of conservation laws of Temple class. In this paper, a continuous semigroup of solutions is constructed on a domain of ${{\bf L}}^\infty$ functions, with possibly unbounded variation. Trajectories depend Lipschitz continuously on the initial data, in the ${{\bf L}}^1$ distance. Moreover, we show that a weak solution of the Cauchy problem coincides with the corresponding semigroup trajectory if and only if it satisfies an entropy condition of Oleinik type, concerning the decay of positive waves.

Citation

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Alberto Bressan. Paola Goatin. "Stability of $L^\infty$ solutions of Temple class systems." Differential Integral Equations 13 (10-12) 1503 - 1528, 2000. https://doi.org/10.57262/die/1356061137

Information

Published: 2000
First available in Project Euclid: 21 December 2012

zbMATH: 1047.35095
MathSciNet: MR1787079
Digital Object Identifier: 10.57262/die/1356061137

Subjects:
Primary: 35L65
Secondary: 35B35

Rights: Copyright © 2000 Khayyam Publishing, Inc.

Vol.13 • No. 10-12 • 2000
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