  In this paper, we analyze a model composed by coupled local and nonlocal
diffusion equations acting in different subdomains. We consider the limit case
when one of the subdomains is thin in one direction (it is concentrated to a
domain of smaller dimension) and as a limit problem we obtain coupling between
local and nonlocal equations acting in domains of different dimension. We find
existence and uniqueness of solutions and we prove several qualitative
properties (like conservation of mass and convergence to the mean value of the
initial condition as time goes to infinity).
