极限方程为混合型的一类三阶偏微分方程的奇摄动

Singular Perturbation of a Class of Third Order Partial Differential Equations under Limit Equation to be Mixed Type

该文研究在部分边界上退化为抛物型的一类三阶偏微分方程的奇摄动,在适当的条件下,导出可解性的充分条件,证得解的存在性,并给出任意阶的一致有效的渐近展开式.

In this paper the singular perturbation of a class of third order partial differential equations degenerating to parabolic type at partial boundary is considered. Under appropriate conditions, a sufficient condition of solvability is derived, the existence of solution is proved and the uniformly valid asymptotic expansion of arbitray order is given as well.