  In this paper, we present an analytical study, in the one space dimensional
case, of the fluid dynamics system proposed in [4] to model the formation of
biofilms. After showing the hyperbolicity of the system, we show that, in a
open neighborhood of the physical parameters, the system is totally dissipative
near its unique non vanishing equilibrium point. Using this property, we are
able to prove existence and uniqueness of global smooth solutions to the Cauchy
problem on the whole line for small perturbations of this equilibrium point and
the solutions are shown to converge exponentially in time at the equilibrium
state.
