J4 ›› 2010, Vol. 48 ›› Issue (1): 52-56.

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InfinitelyLarge Initial Value Problem for a Class ofQuasi-Linear Singular Perturbed Equation

WANG Aifeng1,2, NI Mingkang2   

  1. 1. School of Mathematical Science, Huaiyin Normal University, Huaian 223001, Anhui Province, China|2. Department of Mathematics, School of Science and Engineering, East China Normal University, Shanghai 200062, China
  • Received:2009-01-10 Online:2010-01-26 Published:2010-01-27
  • Contact: NI Mingkang E-mail:xiaovikdo@163.com.

Abstract:

A class of infinitelylarge initial value problem was considered for the quasilinear singular perturbed equation. Via a simple transformation, this equation was transformed into Tihonov system. Under suitable conditions, we constructed its formula solution using the method of boundary functions. At the same time, the (n+1)th order asymptotic solution of the problem was given in the whole interval.

Key words: infinitelylarge solution, singular perturbation, quasilinear

CLC Number: 

  • O175.14