Differential and Integral Equations

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

Alberto Bressan and Paola Goatin

Full-text: Open access


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

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

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

Export citation