00947nas a2200121   4500008004300000245005900043210005800102260002300160520056700183100002100750700001800771856003600789       2000                        en_Ud  00aStability of L^infty Solutions of Temple Class Systems0 aStability of Linfty Solutions of Temple Class Systems  bKhayyam Publishing3 a<p>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.</p>1 aBressan, Alberto1 aGoatin, Paola  uhttp://hdl.handle.net/1963/325600990nas a2200121   4500008004300000245007000043210006900113260001300182520059800195100002100793700001800814856003600832       1999                        en_Ud  00aOleinik type estimates and uniqueness for n x n conservation laws0 aOleinik type estimates and uniqueness for n x n conservation law  bElsevier3 aLet $u_t+f(u)_x=0$ be a strictly hyperbolic $n\\\\times n$ system of conservation laws in one space dimension. Relying on the existence of a semigroup of solutions, we first establish the uniqueness of entropy admissible weak solutions to the Cauchy problem, under a mild assumption on the local oscillation of $u$ in a forward neighborhood of each point in the $t\\\\text{-}x$ plane. In turn, this yields the uniqueness of weak solutions which satisfy a decay estimate on positive waves of genuinely nonlinear families, thus extending a classical result proved by Oleĭnik in the scalar case.1 aBressan, Alberto1 aGoatin, Paola  uhttp://hdl.handle.net/1963/3375