@article {1998,
title = {Uniqueness for discontinuous ODE and conservation laws},
journal = {Nonlinear Analysis 34 (1998) 637-652},
number = {SISSA;26/97/M},
year = {1998},
publisher = {Elsevier},
abstract = {Consider a scalar O.D.E. of the form $\\\\dot x=f(t,x),$ where $f$ is possibly discontinuous w.r.t. both variables $t,x$. Under suitable assumptions, we prove that the corresponding Cauchy problem admits a unique solution, which depends H\\\\\\\"older continuously on the initial data.\\nOur result applies in particular to the case where $f$ can be written in the form $f(t,x)\\\\doteq g\\\\big( u(t,x)\\\\big)$, for some function $g$ and some solution $u$ of a scalar conservation law, say $u_t+F(u)_x=0$. In turn, this yields the uniqueness and continuous dependence of solutions to a class of $2\\\\times 2$ strictly hyperbolic systems, with initial data in $\\\\L^\\\\infty$.},
doi = {10.1016/S0362-546X(97)00590-7},
url = {http://hdl.handle.net/1963/3699},
author = {Alberto Bressan and Wen Shen}
}