极限方程为椭圆-抛物的四阶椭圆型方程的奇摄动

Singular Perturbation of the Fourth Order Elliptic Equation When the Limit Equation Is Elliptic-Parabolic

本文研究了极限方程为椭圆-抛物的四阶椭圆型方程-ε~2△~2u+y^m(?)+(?)+a(x,y)(?)+b(x,y)(?)+c(x,y)=0的奇摄动问题,其中ε为正的小参数,m为正的实数,Δ为拉普拉斯算子,a,b,c充分光滑.在适当的假设下,导出可解性的充分条件,证明了解的存在和给出任意阶的一致有效的渐近解.

In this paper we consider the singular perturbation of the fourth order elliptic equation = 0 when the limit equation is elliptic-parabolic, where ε is a positive parameter, m is a positive real number, Δ 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.