FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2000, VOLUME 6, NUMBER 3, PAGES 723-738

**Asymptotics of the solution of a system of equations in
partial derivatives of the first order with a small
parameter at some derivatives**

V. F. Butuzov

A. F. Karaschuk

Abstract

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A system of two singularly perturbed equations in partial
derivatives of the first order on a plane with
a nonlinear right side is considered.
A small parameter enters the equations as a multiplier
at partial derivatives on different arguments.
The theorem of existence of the classical solution of this
system with additional conditions on axes of coordinates is proved and
asymptotic approximation of any order of the small parameter is
constructed.

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Last modified: December 8, 2000