  We derive conditions for well-posedness of semilinear evolution equations
with unbounded input operators. Based on this, we provide sufficient conditions
for such properties of the flow map as Lipschitz continuity,
bounded-implies-continuation property, boundedness of reachability sets, etc.
These properties represent a basic toolbox for stability and robustness
analysis of semilinear boundary control systems.
  We cover systems governed by general $C_0$-semigroups, and analytic
semigroups that may have both boundary and distributed disturbances. We
illustrate our findings on an example of a Burgers' equation with nonlinear
local dynamics and both distributed and boundary disturbances.
