Journal of East China Normal University(Natural Sc ›› 2017, Vol. ›› Issue (3): 39-47.doi: 10.3969/j.issn.1000-5641.2017.03.004

• Mathematics • Previous Articles     Next Articles

A class of singularly perturbed hyperbolic nonlinear integral-differential system

FENG Yi-hu1, MO Jia-qi2   

  1. 1. Department of Electronics and Information Engineering, Bozhou College, Bozhou Anhui 236800, China;
    2. Department of Mathematics, Anhui Normal University, Wuhu Anhui 241003, China
  • Received:2016-03-17 Online:2017-05-25 Published:2017-05-18

Abstract: A class of singularly perturbed system for the hyperbolic nonlinear integral-differential system is considered. Firstly, the outer solution to system is obtained by employing the Fredholm type integral equation. Then the boundary layer corrective term is constructed using the variables of multiple scales method. And the initial layer corrective term is found via the stretched variable method. Finally, from the fixed point theory, the uniformly valid behavior for the composed asymptotic expansion of singular perturbation solution is proved.

Key words: integral-differential equation, singular perturbation, hyperbolic type equation

CLC Number: