Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Chinese Journal of Engineering Mathematics ›› 2015, Vol. 32 ›› Issue (5): 783-790.doi: 10.3969/j.issn.1005-3085.2015.05.015

Previous Articles    

Analyticity and Persistence Properties of Solutions to the Fornberg-Whitham Equation

ZHAO Cai-xia1,2,   FU Ying1   

  1. 1- School of Mathematics, Northwest University, Xi'an 710127
    2- Experimental Middle School of Xinzhou of Shanxi Province, Xinzhou 034000
  • Received:2013-06-17 Accepted:2014-06-23 Online:2015-10-15 Published:2015-12-15
  • Supported by:
    The National Natural Science Foundation of China (11001219; 11471259); the Natural Science Foundation of Shaanxi Province (2014JQ1002).

Abstract:

The long time behavior of solutions is one of important problems in the study of partial differential equations. To a great degree, the properties of solutions will depend on those of initial values. In this paper, the analyticity and persistence properties of solutions to the Cauchy problem of the Fornberg-Whitham equation are considered respectively when the initial values are analytic or decaying. It is shown that the solutions of this equation are analytic in both variables, globally in space and locally in time. The solutions uniformly have the same decay property at any later time when the initial datum decays at infinity.

Key words: Fornberg-Whitham equation, analytic solutions, persistence property

CLC Number: