  The purpose of this paper is to mathematically investigate the formation of a
plasma sheath near the surface of walls immersed in a plasma, and to analyze
qualitative information of such a sheath layer. In the case of planar wall,
Bohm proposed a criterion on the velocity of the positive ion for the formation
of sheath, and several works gave its mathematical validation. It is of more
interest to analyze the criterion for the nonplanar wall. In this paper, we
study the existence and asymptotic stability of stationary solutions for the
Euler-Poisson equations in a domain of which boundary is drawn by a graph. The
existence and stability theorems are shown by assuming that the velocity of the
positive ion satisfies the Bohm criterion at infinite distance. What most
interests us in these theorems is that the criterion together with a suitable
necessary condition guarantees the formation of sheaths as long as the shape of
walls is drawn by a graph.
