数学物理学报 ›› 2016, Vol. 36 ›› Issue (6): 1211-1220.

• 论文 • 上一篇    

位势井及其对具临界初始能量的非牛顿渗流方程的应用

刘洋   

  1. 西北民族大学数学与计算机科学学院 兰州 730124
  • 收稿日期:2016-03-28 修回日期:2016-08-12 出版日期:2016-12-26 发布日期:2016-12-26
  • 作者简介:刘洋,liuyangnufn@163.com
  • 基金资助:

    国家自然科学基金(41465002)和中央高校基本科研业务费专项资金(31920150036)资助

Potential Well and Application to Non-Newtonian Filtration Equations at Critical Initial Energy Level

Liu Yang   

  1. College of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou 730124
  • Received:2016-03-28 Revised:2016-08-12 Online:2016-12-26 Published:2016-12-26
  • Supported by:

    Supported by the NSFC (41465002) and the Fundamental Research Funds for the Central Universities (31920150036)

摘要:

该文研究具临界初始能量的非牛顿渗流方程的初边值问题.通过构建新的位势井及其井外集合并证明它们的不变性,得到了解的整体存在性与有限时间爆破.

关键词: 非牛顿渗流方程, 整体存在性, 有限时间爆破, 位势井, 临界初始能量

Abstract:

This paper is concerned with the initial boundary value problem of non-Newtonian filtration equations at critical initial energy level. We first construct a new potential well and its outside set, and prove their invariance. Furthermore, the global existence and finite time blow-up of solutions are obtained.

Key words: Non-Newtonian filtration equations, Global existence, Finite time blow-up, Potential well, Critical initial energy

中图分类号: 

  • O175.29