Shadowing and the plasma-sheath transition layer

This paper gives a rigorous derivation of the System mu (2) d(2)w(0)/d zeta (2) = w(0)(2) + zeta, w(0)(zeta (0)) = -(-zeta (0))(1/2), dw(0)/d zeta (ze ta (0)) = 1/2(-zeta (0))(-1/2), zeta (0) < 0, governing the electric potent ial. in the transition layer joining quasi-neutral plasma to space charge s heath in a weakly ionized plasma. The parameter <mu> represents the toleran ce for "shadowing," i.e., it measures the "distance" between the true solut ion of the full Euler-Poisson system and the solution of the reduced order limit equation for w(0)(zeta).