@article {2000, title = {Stability of L^infty Solutions of Temple Class Systems}, journal = {Differential Integral Equations 13 (2000) 1503-1528}, number = {SISSA;134/98/M}, year = {2000}, publisher = {Khayyam Publishing}, 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 $L^\infty$ 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.

}, url = {http://hdl.handle.net/1963/3256}, author = {Alberto Bressan and Paola Goatin} }