局部任意阶增长的拟线性抛物方程解的存在性  

Global Existence for Some Quasi-Linear Parabolic Equations with Locally Arbitrary Growth and Memory

作　　者：马文雅[1] 张乔夫[2,3] 崔俊芝[4] 

机构地区：[1]河南农业大学信息与管理科学学院,郑州450002 [2]浙江大学电气工程学院,杭州310027 [3]宁波鑫高益公司,浙江余姚315400 [4]中国科学院计算数学与科学工程计算研究所,北京100190

出　　处：《数学物理学报（A辑）》2015年第5期833-844,共12页Acta Mathematica Scientia

基　　金：国家重点基础研究发展计划(973计划)项目(2012CB025904);国家自然科学基金(90916027);NSFC-河南人才培养联合基金(U1404102)资助

摘　　要：该文运用Schauder不动点方法对一类具有局部任意阶增长、含有记忆项的拟线性抛物方程证明了全局弱解的存在性.具体地,通过固定系数及源项中的函数变量构造一个线性映射,其定义域取值范围是有界的,但可以局部任意阶增长.由极值原理知其值域包含在一个有界凸集中,又注意到解关于数据的连续依赖性,所以该映射是连续的,结合紧性得知存在不动点.证明中仅要求系数关于函数变量连续,关于时空变量可测即可.另外,对含记忆项的情形也进行了考察.Existence theory for a kind of quasi-linear parabolic equations is established by the Schauder fixed point method.Actually a linearized map is defined by fixing the function variables in the coefficients and the right-hand term.Its domain is chosen to be bounded but a locally arbitrary growth condition is considered.Therefore its range is contained in a closed convex set through the maximum principle.This map is continuous since the solution smoothly depends on the data.Compactness is deduced from the embedding theorem,so there exists a fixed point.The coefficients are just required to be continuous with respect to the function variables,but can be only measurable with respect to the space and time variables.Moreover,memory terms are also considered.

关 键 词：拟线性抛物方程 不动点 存在性 局部任意阶增长 

分 类 号：O175.29[理学—数学]