一类带有阻尼项Burgers方程的Cauchy问题  

On Cauchy Problem for a Burgers Equation with Damping Term

作　　者：李晓营[1] 林春进 徐国静[2] LI Xiao-ying;LIN Chun-jin;XU Guo-jing(College of science,Hehai University,Nanjing 211100,China;Department of Mathematics Teaching and Research of Basic,Wentian College,Hehai University,Ma anshan Anhui 243031,China)

机构地区：[1]河海大学理学院,南京211100 [2]河海大学文天学院基础部数学教研室,安徽马鞍山243031

出　　处：《西南师范大学学报（自然科学版）》2018年第4期20-23,共4页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11201116)

摘　　要：用特征线方法研究带有阻尼项Burgers方程的Cauchy问题解的存在性及有限时间爆破的情况.借助于初始数据,给出了解的表达式.利用隐函数,获得了解关于时间变量、空间变量的一阶偏导数,并讨论了这些偏导数在有限时间内爆破的充分必要条件.The global existence and the finite time blowup of the solutions to the Cauchy problem of Burgers equation with damping term are studied in this paper by the method of characteristics.The solutions are expressed by the initial data.The first order partial derivatives about time and space variables of the solution are obtained by using implicit functions,and the necessary and sufficient conditions for blowup of the solutions are given.

关 键 词：阻尼项 特征线方法 BURGERS方程 爆破 

分 类 号：O175.22[理学—数学]