On the shift differentiability of the flow generated by a hyperbolic system of conservation laws
Stefano Bianchini  S.I.S.S.A. (I.S.A.S.), Via Beirut 2/4, 34013 Trieste, Italy (email) Abstract:
We consider the notion of shift tangent vector introduced in [7] for
real valued BV functions and introduced in [9] for vector valued BV functions.
These tangent vectors act on a function $u\in L^1$ shifting horizontally the points
of its graph at different rates, generating in such a way a continuous path in $L^1$. The main result of [7] is that
if the semigroup $\mathcal S$ generated by a scalar
strictly convex conservation law is shift differentiable, i.e. paths generated by
shift tangent vectors at $u_0$ are mapped in paths generated by shift tangent
vectors at $\mathcal S_t u_0$ for almost every $t\geq 0$.
This leads to the introduction of a sort
of differential, the "shift differential",
of the map $u_0 \to \mathcal S_t u_0$.
Keywords: Shift differential, hyperbolic conservation laws, ﬂow generated by a hyperbolic system.
Received: July 1999; Revised: September 1999; Available Online: January 2000. 
2014 IF (1 year).972
