Singular perturbation of linear partial differential equation with constant coefficients

Hussain Sayid Nur

Vol. 30 (1969), No. 1, 187–199

DOI: 10.2140/pjm.1969.30.187

Abstract

Let P_j(z,𝜖) be a polynomial in z and 𝜖 with complex coefficients, where z is in E^m and 𝜖 > 0 is a small parameter. Let L_𝜖 = ∑ _j=0^lP_l−j(∂_x,𝜖)(δ_t)^g be a polynomial in δ_t,δ_x and 𝜖, which is not divisible by the square of a similar nonconstant polynomial. We shall assume that P₀(z,𝜖) = 𝜖 and P₁(z) is independent of 𝜖.

In this paper we shall show that under certain conditions the solution u₈(t,x) of L_𝜖(u) = f_𝜖(t,x) converges to the solution u₀(t,x) of L₀(u) = f₀(t,x).

Mathematical Subject Classification

Primary: 35.14

Milestones

Received: 13 April 1967

Revised: 27 September 1968

Published: 1 July 1969