A SINGULAR SINGULARLY PERTURBED BOUNDARY-VALUE PROBLEM OF THE 2ND-ORDER QUASI-LINEAR SYSTEMS

[摘要] The singular singularly perturbed boundary value problem epsilon d2x/dt2 = A(x, t)dx/dt + B(x, t), x(0, epsilon) = alpha(epsilon), epsilon[a dx(0, epsilon)/dt + b dx(1, epsilon)/dt] = beta(epsilon) for an m-dimensional system of quasilinear differential equations is considered under the assumption that there is a vector-valued function F(x, t) such that del(x)F(x, t) = A(x, t). The asymptotic solution is constructed by a modified Vasil'eva method where there are 3 boundary layer corrections, i.e., the left boundary layer contains 2 different stretched variables t/square-root epsilon and t/epsilon. The existence and uniqueness of the exact solution and the uniform validity of the formal asymptotic solution for the boundary value problem are proved by using the Banach-Picard fixed-point theorem. (C) 1994 Academic Press, Inc.

[发布日期] 1994-03-01