On a Class of High-Order Nonlinear Singular Perturbed Nonlocal Systems’ Steady State Robin Problem

XU Jianzhong; WANG Weigang; MO Jiaqi

doi:10.21656/1000-0887.410049

Volume 41 Issue 11

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XU Jianzhong, WANG Weigang, MO Jiaqi. On a Class of High-Order Nonlinear Singular Perturbed Nonlocal Systems’ Steady State Robin Problem[J]. Applied Mathematics and Mechanics, 2020, 41(11): 1284-1291. doi: 10.21656/1000-0887.410049

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On a Class of High-Order Nonlinear Singular Perturbed Nonlocal Systems’ Steady State Robin Problem

doi: 10.21656/1000-0887.410049

¹Department of Electronics and Information Engineering, Bozhou University, Bozhou, Anhui 236800, P.R.China;²Department of Basic, Hefei Preschool Education College, Hefei 230011, P.R.China;³School of Mathematics & Statistics, Anhui Normal University, Wuhu, Anhui 241003, P.R.China

Funds: The National Natural Science Foundation of China(11771005)

Received Date: 2020-02-07
Publish Date: 2020-11-01

Abstract

Abstract

A class of high-order nonlinear integral-differential singular perturbation systems’ steady state Robin problem was discussed. Firstly, the theory of differential inequality for the high-order nonlinear nonlocal differential system was built. Then, the outer solution to the problem was structured and the boundary layer corrective term was obtained by means of the local coordinate system. Thus the formal asymptotic expansion of the solution was got. Finally, the uniform validity of the asymptotic expansion of the solution was proved with the theory of differential inequality.
- singular perturbation,
- steady state,
- nonlocal

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References

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