In this paper, we develop and analyze
the Runge-Kutta discontinuous Galerkin
(RKDG) method to solve weakly coupled hyperbolic
multi-domain problems. Such problems involve transfer type
boundary conditions with discontinuous fluxes
between different domains, calling for
special techniques to prove stability of the RKDG methods.
We prove both stability and error estimates for our
RKDG methods on simple models, and then apply them to a
biological cell proliferation model \cite{EMSC}. Numerical
results are provided to illustrate the good behavior of
our RKDG methods.