FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 5, PAGES 21-28

**On systems of two singularly perturbed quasilinear second-order
equations**

A. B. Vasil'eva

Abstract

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A system of two quasilinear second-order equations with
a small parameter standing by the second derivatives is studied.
The cases where the matrix of coefficients of the first derivatives
has the following eigenvalues are considered: (a) both of them
have negative real parts; (b) they are of opposite sign;
(c) one of them is equal to zero.
To find a solution and its asymptotics, the initial-value or
boundary-value problems are posed depending on the form of these
eigenvalues.

Location: http://mech.math.msu.su/~fpm/eng/k06/k065/k06503h.htm

Last modified: February 21, 2007