Differential and Integral Equations

Stability of $L^\infty$ solutions of Temple class systems

Alberto Bressan and Paola Goatin

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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.

Article information

Source
Differential Integral Equations Volume 13, Number 10-12 (2000), 1503-1528.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356061137

Mathematical Reviews number (MathSciNet)
MR1787079

Zentralblatt MATH identifier
1047.35095

Subjects
Primary: 35L65: Conservation laws
Secondary: 35B35: Stability

Citation

Bressan, Alberto; Goatin, Paola. Stability of $L^\infty$ solutions of Temple class systems. Differential Integral Equations 13 (2000), no. 10-12, 1503--1528. https://projecteuclid.org/euclid.die/1356061137.


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