  This work contributes to an understanding of the domain size's effect on the
existence and uniqueness of the linear convection--diffusion equation with
integral-type boundary conditions, where boundary conditions depend non-locally
on unknown solutions. Generally, the uniqueness result of this type of equation
is unclear. In this preliminary study, a uniqueness result is verified when the
domain is sufficiently large or small. The main approach has an advantage of
transforming the integral boundary conditions into new Dirichlet boundary
conditions so that we can obtain refined estimates, and the comparison theorem
can be applied to the equations. Furthermore, we show a domain such that under
different boundary data, the equation in this domain can have infinitely
numerous solutions or no solution.
