数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (3): 843-856.doi: 10.1016/S0252-9602(11)60281-6

• 论文 • 上一篇    下一篇

MULTISCALE HOMOGENIZATION OF NONLINEAR HYPERBOLIC EQUATIONS WITH SEVERAL TIME SCALES

Jean Louis Woukeng, David Dongo   

  1. Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, Box 67, Dschang, Cameroon
  • 收稿日期:2009-07-20 修回日期:2010-01-01 出版日期:2011-05-20 发布日期:2011-05-20

MULTISCALE HOMOGENIZATION OF NONLINEAR HYPERBOLIC EQUATIONS WITH SEVERAL TIME SCALES

Jean Louis Woukeng, David Dongo   

  1. Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, Box 67, Dschang, Cameroon
  • Received:2009-07-20 Revised:2010-01-01 Online:2011-05-20 Published:2011-05-20

摘要:

We study the multiscale homogenization of a nonlinear hyperbolic equation in a periodic setting. We obtain an accurate omogenization result. We also show that as the nonlinear term depends on the microscopic time variable, the global homogenized problem thus obtained is a system consisting of two hyperbolic equations. It is also shown that in spite of the presence of several time scales, the global homogenized problem is not a reiterated one.

关键词: hyperbolic, multiscale, nonlinear

Abstract:

We study the multiscale homogenization of a nonlinear hyperbolic equation in a periodic setting. We obtain an accurate omogenization result. We also show that as the nonlinear term depends on the microscopic time variable, the global homogenized problem thus obtained is a system consisting of two hyperbolic equations. It is also shown that in spite of the presence of several time scales, the global homogenized problem is not a reiterated one.

Key words: hyperbolic, multiscale, nonlinear

中图分类号: 

  • 35B27