$C_0$-semigroups for hyperbolic partial differential equations on a   one-dimensional spatial domain
  Hyperbolic partial differential equations on a one-dimensional spatial domain are studied. This class of systems includes models of beams and waves as well as the transport equation and networks of non-homogeneous transmission lines. The main result of this paper is a simple test for $C_0$-semigroup generation in terms of the boundary conditions. The result is illustrated with several examples. 
Birgit Jacob, Kirsten Morris, Hans Zwart
math.AP math.FA