具有超抛物型极限方程的非线性奇摄动反应扩散问题(英文)  

Nonlinear Singularly Perturbed Reaction Diffusion Problems With Ultra Parabolic Limiting Equations

作　　者：莫嘉琪[1] 

机构地区：[1]安徽师范大学数学系

出　　处：《数学进展》2008年第1期85-91,共7页Advances in Mathematics（China）

基　　金：Supported by the NSFC(No．40676016，10471039);the National Key Project for Basics Research(No．2003CB415101-03 and No．2004CB418304);the Key Project of the Chinese Academy of Sciences(No．KZCX3-SW-221);in part by E-Institutes of Shanghai Municipal Education Commission(No．E03004)．

摘　　要：讨论了一类具有超抛物型方程的反应扩散问题.首先,证明了比较定理.其次,构造了形式渐近解.然后,利用微分不等式方法,研究了问题解的存在、唯一性和渐近性态.最后得到了原问题解的渐近展开式.The reaction diffusion problems with ultra parabolic equations are considered. Firstly, a comparison theorem is proved. Secondly, a formal asymptotic solution is constructed. Thirdly, by using the differential inequalities method, the existence, uniqueness and its asymptotic behavior of solution for the problem are studied. Finally, the uniformly valid asymptotic expansion of the solution for the original problem is obtained.

关 键 词：超抛物型方程 奇摄动 反应扩散 渐近性态 比较定理 

分 类 号：O175.29[理学—数学]