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Applied Mathematics and Mechanics (English Edition) ›› 1991, Vol. 12 ›› Issue (1): 77-84.

• 论文 • 上一篇    下一篇

SINGULAR PERTURBATION OF THE FOURTH ORDER ELLIPTIC EQUATION WHEN THE LIMIT EQUATION IS ELLIPTIC-PARABOLIC

林宗池   

  1. Department of Mathematics, Fujian Normal University, Fuzhou
  • 收稿日期:1990-02-15 出版日期:1991-01-18 发布日期:1991-01-18
  • 基金资助:

    National Natural Science Foundation of China(Ⅰ)

SINGULAR PERTURBATION OF THE FOURTH ORDER ELLIPTIC EQUATION WHEN THE LIMIT EQUATION IS ELLIPTIC-PARABOLIC

Lin Zong-chi   

  1. Department of Mathematics, Fujian Normal University, Fuzhou
  • Received:1990-02-15 Online:1991-01-18 Published:1991-01-18

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摘要： In this paper we cosider the singular perturbation of the fourth order elliptic equation -ε2Δ2u+ym∂2u/∂y2+a(x,y)∂u/∂y+b(x,y)∂u/∂x+c(x,y)=0 when the limit equationis elliptic-parabolic, where e is a positive parameter, Δ is a positive real number, A is Laplacian operator, a,b,c are sufficiently smooth. Under appropriate condition we derive the sufficient condition of solvability and prove the existence of solution and give a uniformly valid asymptotic solution of arbitrary order.

Abstract: In this paper we cosider the singular perturbation of the fourth order elliptic equation -ε2Δ2u+ym∂2u/∂y2+a(x,y)∂u/∂y+b(x,y)∂u/∂x+c(x,y)=0 when the limit equationis elliptic-parabolic, where e is a positive parameter, Δ is a positive real number, A is Laplacian operator, a,b,c are sufficiently smooth. Under appropriate condition we derive the sufficient condition of solvability and prove the existence of solution and give a uniformly valid asymptotic solution of arbitrary order.

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