具有粘性解的二维Field-Noyes方程的Cauchy问题  

The Cauchy Problem of Two Dimensional Field-Noyes Equation with Viscous Solutions

作　　者：王婷婷 WANG Ting-ting(College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China)

机构地区：[1]南京航空航天大学理学院,南京210016

出　　处：《西安文理学院学报（自然科学版）》2021年第2期6-11,22,共7页Journal of Xi’an University(Natural Science Edition)

摘　　要：讨论了具有粘性解的二维Field-Noyes方程的Cauchy问题,为研究一般的具有粘性解的方程的Cauchy问题的读者提供参考.首先,利用自相似变换、齐次热方程的基本解、Duhamel原理将原方程化为等价的积分方程.然后,利用Picard迭代技巧证明了解的局部存在性.最后,利用极值原理求出二维Field-Noyes方程的Cauchy问题局部解的L^(∞)估计.根据解的延拓定理,可以证明原问题粘性解的整体存在性.通过本文的研究得到二维Field-Noyes方程的Cauchy问题粘性解的整体存在性.In this paper,the Cauchy problem of two dimensional Field-Noyes equation with viscous solutions is discussed,which provides a reference for readers who study the Cauchy problem of general equation with viscous solution.Firstly,the original equation is transformed into an equivalent integral equation by using self similar transformation,basic solution of homogeneous heat equation and Duhamel principle.Then,Picard iteration technique is used to prove the local existence of the solution.Finally,the L^(∞) estimation of the local solution of the Cauchy problem of the two-dimensional Field-Noyes equation is obtained by using the extremum principle.According to the continuation theorem of the solution,the global existence of the viscous solution of the original problem can be proved.Through this study,the global existence of viscous solutions for the Cauchy problem of two-dimensional Field-Noyes equation is obtained.

关 键 词：Field-Noyes方程 CAUCHY问题 L^(∞)估计 极值原理 解的延拓定理 

分 类 号：O175.2[理学—数学]