Abstract
We consider an initial-boundary value problem for the classical linear wave equation,
where mixed boundary conditions of Dirichlet and Neumann/Robin type are enforced at the endpoints of a bounded interval.
First, by a careful application of the method of characteristics, we derive a closed-form representation
of the solution for an impulsive Dirichlet data at the left endpoint, and valid for either a Neumann or a Robin
data at the right endpoint. Then we devise a reconstruction procedure for identifying both the interval length and
the Robin parameter. We provide a corresponding stability result and verify numerically its performance moving
from a finite element discretization.
Small data blow-up of semi-linear wave equation with scattering dissipation and time-dependent mass
