TY - JOUR
T1 - Uniqueness for discontinuous ODE and conservation laws
JF - Nonlinear Analysis 34 (1998) 637-652
Y1 - 1998
A1 - Alberto Bressan
A1 - Wen Shen
AB - 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 $\\\\L^\\\\infty$.
PB - Elsevier
UR - http://hdl.handle.net/1963/3699
U1 - 606
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -