Vol. 30, No. 1, 1969

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Singular perturbation of linear partial differential equation with constant coefficients

Hussain Sayid Nur

Vol. 30 (1969), No. 1, 187–199
Abstract

Let Pj(z,𝜖) be a polynomial in z and 𝜖 with complex coefficients, where z is in Em and 𝜖 > 0 is a small parameter. Let L𝜖 = j=0lPlj(x,𝜖)(δt)g be a polynomial in δtx 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 L𝜖(u) = f𝜖(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
Authors
Hussain Sayid Nur