  The adsorption phenomenon of neutral particles from the limiting surfaces of
the sample in the Langmuir approximation is investigated. The diffusion
equation regulating the redistribution of particles in the bulk is assumed to
be of hyperbolic type, in order to take into account the finite velocity of
propagation of the density variations. We show that in this framework the
condition on the conservation of the number of particles gives rise to a
nonlocal boundary condition. We solve the partial differential equation
relevant to the diffusion of particles by means of the separation of variables,
and present how it is possible to obtain approximated eigenvalues contributing
to the solution. The same problem is faced numerically by a finite difference
algorithm. The time dependence of the surface density of adsorbed particles is
deduced by means of the kinetic equation at the interface. The predicted
non-monotonic behavior of the surface density versus the time is in agreement
with experimental observations reported in the literature, and is related to
the finite velocity of propagation of the density variations.
