Recently I am reading a paper "Global solution and smoothing effect for a non-local regularization of a hyperbolic equation" published on J.E.E, 2004. In the proof, the authors write "It is classical that the solution to an hyperbolic equation equation is Lipschitz -continuous $[0,\infty)\to L^1(\mathbb{R})$". But I can not understand. Who has some ideas? I have read the reference paper "First order quasi-linear equations in several independent variables" by S.N.Kruzkov, but I can not find this fact.
