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
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摘要: 本文研究了极限方程为椭圆-抛物的四阶椭圆型方程-ε2Δ2u+ym∂2u/∂y2+∂2u/∂x2+a(x,y)∂u/∂y+b(x,y)∂u/∂x+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.Abstract: In this paper we cosider the singular perturbation of the fourth order elliptic equation-ε2Δ2u+ym∂2u/∂y2+∂2u/∂x2+a(x,y)∂u/∂y+b(x,y)∂u/∂x+c(x,y)=0 when the limit equationis elliptic-parabolic, where ε 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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Key words:
- Singular perturbation /
- limit equation /
- elliptic equation
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