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Applied Mathematics and Mechanics (English Edition) ›› 2010, Vol. 31 ›› Issue (6): 769-774.doi: https://doi.org/10.1007/s10483-010-1311-6

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Singularly perturbed reaction diffusion equations with time delay

MO Jia-Qi1,2, WEN Zhao-Hui3   

  1. 1. Department of Mathematics, Anhui Normal University, Wuhu 241000, Anhui Province, P. R. China;
    2. Division of Computational Science, E-Institute of Shanghai Universities at SJTU, Shanghai 200240, P. R. China;
    3. Institute of Applied Mathematics, School of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu 233030, Anhui Province, P. R. China
  • Received:2010-03-02 Revised:2010-05-08 Online:2010-06-01 Published:2010-06-01

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Abstract: A class of initial boundary value problems of differential-difference equations for reaction diffusion with a small time delay is considered. Under suitable conditions and by using the stretched variable method, a formal asymptotic solution is constructed. Then, by use of the theory of differential inequalities, the uniform validity of the solution is proved.

Key words: nonlinear, reaction diffusion, singular perturbation, time delay

2010 MSC Number: 

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