The Generalized Spike Layer Solution to Singular Perturbation Nonlinear Parabolic System with Two Parameters
FENG Yihu1,2, HOU Lei2, MO Jiaqi3
1. Department of Electronics and Information Engineering, Bozhou University, Bozhou 236800, China; 2. Department of mathematics, Shanghai University, Shanghai 200436, China; 3. School of Mathematics & Statistics, Anhui Normal University, Wuhu 241003, China
Abstract：A nonlinear parabolic differential system to the singular perturbation problem is studied in this paper. First the outer solution is structured by using the singular perturbation method. Second the spike layer corrective, boundary layer corrective and initial layer corrective terms are obtained by using the multiple scales and stretched variable methods respectively. Final the asymptotic expansion of the generalized solution is obtained. Using the fixed point theorem, the uniform validity for the asymptotic solution is proved. And the asymptotic solution can also carry on analytical operation. So it is known more characters for the generalized solution. Thus it possesses better applied foreground.
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2020, Vol. 43 
