摘要
A class of singular perturbation boundary problem of elliptic equation for higher order is studied. Firstly, under suitable conditions, the generalized outer solution to reduced problems is considered. Then the generalized interior shock asymptotic solution to original problem is constructed by using the theory of generalized functions. Finally, using the fixed point theorem of functional analytic, the uniformly validity of the generalized asymptotic solution with interior shock and boundary layers is proved.
A class of singular perturbation boundary problem of elliptic equation for higher order is studied. Firstly, under suitable conditions, the generalized outer solution to reduced problems is considered. Then the generalized interior shock asymptotic solution to original problem is constructed by using the theory of generalized functions. Finally, using the fixed point theorem of functional analytic, the uniformly validity of the generalized asymptotic solution with interior shock and boundary layers is proved.
基金
Supported by the National Natural Science Foundation of China(41275062,11202106)
the Natural Science Foundation of the Education Department of Anhui Province(KJ2015A418,KJ2015A347)
the Natural Sciences Foundation from the Universities of Jiangsu Province(13KJB170016)
