Evolution family
= Evolution family
{title2=$U(t,s)$}
An evolution family consists of bounded operators $U(t,s)$ for $s\leq t$ satisfying $U(s,s)=I$ and $U(t,r)U(r,s)=U(t,s)$. For sufficiently regular data it solves $\partial_tU(t,s)x=A(t)U(t,s)x$ and $\partial_sU(t,s)x=-U(t,s)A(s)x$.
= Solution operator for a nonautonomous evolution equation
{synonym}