具有非单调过渡层性质的奇摄动半线性边值问题  

Singularly Perturbed Semilinear Boundary Value Problems with Nonmonotone Transition Layer Properties

作　　者：刘树德[1] 叶珊珊[2] 王丹凤[2] 

机构地区：[1]安徽工程大学机电学院,芜湖241000 [2]安徽师范大学数学系,芜湖241000

出　　处：《工程数学学报》2014年第6期872-878,共7页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11202106);安徽高校省级自然科学基金(KJ2011A135)~~

摘　　要：本文在方程的一阶导数项的系数有一个简单零点,即方程有转向点的假设下研究了一类具有非单调过渡层性质的奇摄动半线性边值问题.先用合成展开法构造出问题的形式近似,然后利用衔接法将左、右两边分别具有尖层性质和边界层性质的近似式光滑地衔接起来,从而形成具有非单调过渡层性质的近似,并应用微分不等式理论证明了解的存在性及其渐近性质.Some singularly perturbed semilinear boundary value problems with nonmonotone transition layer properties are studied under the assumption that the coeflicient of the first derivative term in the equation has a simple zero point, i.e., this equation has a turning point. The formal approximation of the problem is constructed using the method of composite expan-sions, and then we joint smoothly by the joint method approximate expressions of left and right sides which exhibit spike layer behavior and boundary layer behavior, respectively. As a result, an approximation which exhibits nonmonotone transition behavior is formed. Finally, the exis-tence and asymptotic behavior of solutions are proved by theory of differential inequalities.

关 键 词：奇摄动 边值问题 非单调过渡层 合成展开法 微分不等式 

分 类 号：O175.14[理学—数学]