The properties of a plasma injected into an insulator or semiconductor are analytically describable if diffusive current flow is neglected. However it is known from experimental and theoretical (computer) studies that the corrections imposed by the dominance of diffusive current flow near the contacts are quite large forL/La<10 and significant even for largerL/La, whereLis the distance between the injecting contacts andLathe ambipolar diffusion length. The regional approximation method is employed to obtain an approximate, but complete analytical description of the injected plasma for the two problems. Satisfactory agreement is obtained with previous computer results of Baron.