Generalized Solutions to Nonlinear Nonlocal Singularly Perturbed Parabolic Initial-Boundary Problems With Two Parameters

FENG Yi-hu; MO Jia-qi

doi:10.21656/1000-0887.380008

Volume 38 Issue 12

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FENG Yi-hu, MO Jia-qi. Generalized Solutions to Nonlinear Nonlocal Singularly Perturbed Parabolic Initial-Boundary Problems With Two Parameters[J]. Applied Mathematics and Mechanics, 2017, 38(12): 1405-1411. doi: 10.21656/1000-0887.380008

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Generalized Solutions to Nonlinear Nonlocal Singularly Perturbed Parabolic Initial-Boundary Problems With Two Parameters

doi: 10.21656/1000-0887.380008

FENG Yi-hu¹,
MO Jia-qi²

¹Department of Electronics and Information Engineering, Bozhou College, Bozhou, Anhui 236800, P.R.China;²School of Mathematics & Computer Science, Anhui Normal University, Wuhu, Anhui 241003, P.R.China

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

Received Date: 2017-01-19
Rev Recd Date: 2017-03-15
Publish Date: 2017-12-15

Abstract

Abstract

A class of generalized parabolic equation singular perturbation problems were considered. Firstly, under suitable conditions, a class of nonlinear nonlocal generalized parabolic equation initial-boundary value problems with two parameters were raised. Secondly, the existence of solutions to corresponding problems was proved. Next, from the Fredholm integral equation, the outer solutions to the initial-boundary value problems were found, and the boundary and initial layer terms were structured by means of the theory of functional analysis, the stretched variables and the multiscale methods, respectively. Then the formal asymptotic expansion of the problem was obtained. Finally, according to the fixed point theorem, the uniform validity of the asymptotic expansion of generalized solutions to the corresponding nonlinear nonlocal initial-boundary value problems was proved.
- singular perturbation,
- asymptotic expansion,
- uniform validity

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References(13)

References

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