一类带有阻尼项Burgers方程的Cauchy问题
On Cauchy Problem for a Burgers Equation with Damping Term
-
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.Abstract: 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.
-
Key words:
- damping term /
- method of characteristics /
- Burgers equation /
- blowup .
-
-
计量
- 文章访问数: 625
- HTML全文浏览数: 250
- PDF下载数: 0
- 施引文献: 0
下载: