Perturbation Method for a Class of High-Order Nonlinear Reaction Diffusion Equations With Double Parameters

WANG Wei-gang; XU Yong-hong; SHI Lan-fang; MO Jia-qi

doi:10.3879/j.issn.1000-0887.2014.12.010

Volume 35 Issue 12

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Article Navigation > Applied Mathematics and Mechanics > 2014 > 35(12): 1383-1391

WANG Wei-gang, XU Yong-hong, SHI Lan-fang, MO Jia-qi. Perturbation Method for a Class of High-Order Nonlinear Reaction Diffusion Equations With Double Parameters[J]. Applied Mathematics and Mechanics, 2014, 35(12): 1383-1391. doi: 10.3879/j.issn.1000-0887.2014.12.010

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Perturbation Method for a Class of High-Order Nonlinear Reaction Diffusion Equations With Double Parameters

doi: 10.3879/j.issn.1000-0887.2014.12.010

¹Tongcheng Teaching Department, Anqing Normal University, Tongcheng, Anhui 231402, P.R.China;²Department of Mathematics and Physics, Bengbu University, Bengbu, Anhui 233030, P.R.China;³College of Mathematics and Statistics, Nanjing University of Information Science & Technology, Nanjing 210044, P.R.China;⁴Department of Mathematics, Anhui Normal University, Wuhu, Anhui 241000, P.R.China

Funds: The National Natural Science Foundation of China（11202106）

Received Date: 2014-08-01
Rev Recd Date: 2014-10-24
Publish Date: 2014-12-15

Abstract

Abstract

The model for a class of highorder nonlinear reaction diffusion singularly perturbed problems with double parameters was addressed. With the singular perturbation method, the structure of the solution to the problem was discussed in the cases of double related small parameters. Firstly, the outer solution to the boundary value problem was given. Secondly, the variable of multiple scales was introduced to obtain the boundary layer correction term for the solution. Then the stretched variable was applied to the boundary neighborhood to get the initial layer correction term. Finally, the theorem of differential inequalities was constructed and the uniformly valid asymptotic expansion of the solution to the problem was proved. The proposed method possesses the advantages of convenient use and high accuracy.
- nonlinear,
- double parameters,
- reaction diffusion

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References(24)

References

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