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

Chinese Journal of Engineering Mathematics ›› 2021, Vol. 38 ›› Issue (4): 564-572.doi: 10.3969/j.issn.1005-3085.2021.04.010

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The Generalized Solution for the Nonlinear Singular Perturbation Robin Problem of Integral-differential Evolution Equation

FENG Yi-hu1,2,   MO Jia-qi3   

  1. 1- Department of Electronics and Information Engineering, Bozhou College, Bozhou 236800
    2- Department of Mathematics, Shanghai University, Shanghai 200436
    3- School of Mathematics & Statistics, Anhui Normal University, Wuhu 241003
  • Received:2019-04-08 Accepted:2020-03-06 Online:2021-08-15 Published:2021-10-15
  • Supported by:
    The National Natural Science Foundation of China (41275062); the Natural Science Foundation of the Education Department of Anhui Province (KJ2017A90; KJ2018A0964); the Key Projects of Outstanding Young Talents of Universities in Anhui Province (gxyqZD2016520); the Key Teaching Project of Anhui Provincial Quality Projects of Colleges and Universities (2018jyxm0594).

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Abstract: A class of generalised nonlinear singular perturbation integral-differential evolution equation Robin problem is discussed. Firstly, the outer solution of the model is obtained by using a solving method of the Fredholm type integral equation. Next, the boundary layer corrective term of the solution is constructed by using the variables of multiple scales. Then the initial layer corrective term of the solution for the original model is found using the stretched variable. And the composed expansion of formal solution for the singular perturbation problem is constructed. Finely, the asymptotic expansion of the generalised solution is proved by using the fixed point theory of the functional analysis.

Key words: singular perturbation, evolution equation, asymptotic solution

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