Solution of A System of Two Partial Differential Equations of the Second Order Using Two Series

Abstract

For a system of two partial differential equations of second order, we obtain and justify twoasymptotics solutions in the form of two series with respect to the small parameter ε . We haveproven the solution is unique and uniform in the domain Ω , and, further, each the asymptoticsapproximations are within O ( ε n +1) .