非线性超抛物型方程广义渐近解的研究  

The study for generalized asymptotic solution to nonlinear ultra parabolic equation

作　　者：韩祥临[1] 莫嘉琪[2] HAN Xian-lin MO Jiq-qi(Faculty of Science, Huzhou University, Huzhou 313000, China School of Mathematics＆ Compoter Science, Anhui Normal University, Wuhu 241003, China)

机构地区：[1]湖州师范学院理学院,浙江湖州313000 [2]安徽师范大学数学计算机科学学院,安徽芜湖241003

出　　处：《高校应用数学学报（A辑）》2017年第2期156-164,共9页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11371248;41275062);浙江省自然科学基金(LY13A010005)

摘　　要：讨论了一类超抛物型方程的非线性奇摄动问题.首先引入了相应问题的比较定理,然后利用奇摄动方法构造了问题的形式渐近解,最后利用比较定理,证明了问题广义解的存在性及其渐近性态.A class of nonlinear singularly perturbed initial-boundary value problem with ultra parabolic equation is considered. Firstly, the comparison theorem is introduced for corresponding prob- lem. Then the formally asymptotic solution is constructed by using the singular perturbation method. Finally, using the comparison theorem, the existence and its asymptotic behavior of generalized solution for the problem are proved.

关 键 词：超抛物型方程 渐近性态 比较定理 

分 类 号：O175.26[理学—数学]