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 (2): 291-297.doi: 10.3969/j.issn.1005-3085.2015.02.013

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Singular Perturbation Problem for Reaction Diffusion Time Delay Equation with Boundary Perturbation

WANG Wei-gang1,   SHI Lan-fang2,   HAN Xiang-lin3,   MO Jia-qi4   

  1. 1- Department of Science and Technology, Tongcheng Teachers College, Tongcheng, Anhui 231400
    2- College of Mathematics and Statistics, Nanjing University of Information Science & Technology, Nanjing, Jiangsu 210044
    3- School of Science, Huzhou University, Huzhou, Zhejiang 313000
    4- Department of Mathematic, Anhui Normal University, Wuhu, Anhui 241003
  • Received:2013-06-25 Accepted:2014-12-26 Online:2015-04-15 Published:2015-06-15
  • Supported by:
    The National Natural Science Foundation of China (11202106); the Natural Science Foundation of the Education Department of Anhui Province (KJ2013A133); the Natural Sciences Fundation from the Universities of Jiangsu Province (13KJB170016); the Natural Science Foundation of Zhejiang Province (LY13A010005). 

Abstract:

The nonlinear singular perturbation problem for the reaction diffusion time delay equation with boundary perturbation is considered in this paper. Firstly, the redu-ced solution is obtained. Secondly, the outer solution of the original problem is constructed. Then, introducing a stretched variable, the initial layer correction of solution is obtained. Finally, under the suitable conditions, applying the theory of differential inequalities the uniformly valid asymptotic expansion of solution for the original initial boundary value problem is proved.

Key words: nonlinear, reaction diffusion, singular perturbation

CLC Number: