  This paper deals with the establishment of Input-to-State Stability (ISS)
estimates for infinite dimensional systems with respect to both boundary and
distributed disturbances. First, a new approach is developed for the
establishment of ISS estimates for a class of Riesz-spectral boundary control
systems satisfying certain eigenvalue constraints. Second, a concept of weak
solutions is introduced in order to relax the disturbances regularity
assumptions required to ensure the existence of classical solutions. The
proposed concept of weak solutions, that applies to a large class of boundary
control systems which is not limited to the Riesz-spectral ones, provides a
natural extension of the concept of both classical and mild solutions. Assuming
that an ISS estimate holds true for classical solutions, we show the existence,
the uniqueness, and the ISS property of the weak solutions.
