You are here

Stability of L^infty Solutions of Temple Class Systems

TitleStability of L^infty Solutions of Temple Class Systems
Publication TypeJournal Article
Year of Publication2000
AuthorsBressan, A, Goatin, P
JournalDifferential Integral Equations 13 (2000) 1503-1528

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 $L^\infty$ functions, with possibly unbounded variation. Trajectories depend Lipschitz continuously on the initial data, in the $L^1$ 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.


Sign in