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)
We consider the notion of shift tangent vector introduced in  for
real valued BV functions and introduced in  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  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.
2015 Impact Factor1.127