非线性边界流下薄膜方程解的存在性  

Existence of A Thin Film Equation with Nnonlinear Boundary Flux

作　　者：王美珊[1] 梁波[1] 沈慧颖[1] 

机构地区：[1]大连交通大学理学院,辽宁大连116028

出　　处：《大连交通大学学报》2014年第2期115-117,共3页Journal of Dalian Jiaotong University

基　　金：国家自然科学基金资助项目(11201045)

摘　　要：研究在非线性边界流条件下,薄膜方程一类非负弱解的存在性,其定义采取分部积分两次来给出.通过构造合适的逼近方程来克服非线性边界流的影响.为获得与逼近参数无关的一致能量估计,需利用熵泛函方法.最后,以紧性定理为基础,获得小参数趋于零的极限,进而证得弱解存在性.The existence of a class of nonegative weak solutions with a nonlinear boundary flux is studied,and the definition is given by applying partial integration twice.By constructing a reasonable approximation problem,the effect of nonlinear boundary is overcomed.In order to obtain the uniform estimates independent of the approximation parameter,the entropy needs to be applied.Finally,the limit of small parameter is gained by compactness theorem,and then the existence is proved.

关 键 词：薄膜方程 非线性边界 存在性 

分 类 号：O175[理学—数学] O411[理学—基础数学]