%0 Journal Article
%J Nonlinear Analysis 34 (1998) 637-652
%D 1998
%T Uniqueness for discontinuous ODE and conservation laws
%A Alberto Bressan
%A Wen Shen
%X 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 $\\\\L^\\\\infty$.
%B Nonlinear Analysis 34 (1998) 637-652
%I Elsevier
%G en_US
%U http://hdl.handle.net/1963/3699
%1 606
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-07-28T09:39:33Z\\nNo. of bitstreams: 1\\nbressan.pdf: 182373 bytes, checksum: 0eb82866d65dea9685ab7ff75c16c0d2 (MD5)
%R 10.1016/S0362-546X(97)00590-7