薄层流中的一类三阶奇摄动边值问题的渐近分析  

Asymptotic Analysis of a Class of Third Order Singularly Perturbed Boundary Value Problem Arising in Thin Film Flows

作　　者：汪志鸣[1] 王隔霞[1] 林武忠[1] 

机构地区：[1]上海华东师范大学数学系,上海200062

出　　处：《应用数学学报》2006年第4期699-706,共8页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10371040);上海市基础研究重点项目(04JC14031)资助项目.

摘　　要：本文研究薄层流中出现的一类三阶奇摄动数学模型．本文不采用研究其渐近等价的二阶奇摄动微分方程的方法,而利用边界层函数法,直接讨论该数学模型的渐近解,并严格地证明了解的存在唯一性和其渐近解的一致有效性．本文的结果不仅去掉了以往方法所必须的位势条件,纠正了某个不适定的假设,而且推广了以往的结果．In this paper, we investigate a class of singularly perturbed third-order boundary value problem, which arises in the thin film flows. Unlike a previous technique to study an asymptotically equivalent second-order problem in stead of the third-order one, we study the mathematical model directly for its asymptotic expansion by the boundary function method and prove the existence and uniqueness of the exact solution of the studied problem as well as the uniform validity of its asymptotic solution in a rigorous way. We completely remove the usual potential condition and correct some error of a certain assumption in the previous literature, under which, the previous result is extended in this paper.

关 键 词：奇摄动 位势条件 边界层函数 

分 类 号：O175.8[理学—数学]