ASYMPTOTICS OF A MULTIZONAL INTERNAL LAYER SOLUTION TO A PIECEWISE-SMOOTH SINGULARLY PERTURBED EQUATION WITH A TRIPLE ROOT OF THE DEGENERATE EQUATION

Qian Yang; Mingkang Ni

doi:10.11948/20210508

2022 Volume 12 Issue 6

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Qian Yang, Mingkang Ni. ASYMPTOTICS OF A MULTIZONAL INTERNAL LAYER SOLUTION TO A PIECEWISE-SMOOTH SINGULARLY PERTURBED EQUATION WITH A TRIPLE ROOT OF THE DEGENERATE EQUATION[J]. Journal of Applied Analysis & Computation, 2022, 12(6): 2441-2457. doi: 10.11948/20210508

Citation:

Qian Yang, Mingkang Ni. ASYMPTOTICS OF A MULTIZONAL INTERNAL LAYER SOLUTION TO A PIECEWISE-SMOOTH SINGULARLY PERTURBED EQUATION WITH A TRIPLE ROOT OF THE DEGENERATE EQUATION[J]. Journal of Applied Analysis & Computation, 2022, 12(6): 2441-2457. doi: 10.11948/20210508

ASYMPTOTICS OF A MULTIZONAL INTERNAL LAYER SOLUTION TO A PIECEWISE-SMOOTH SINGULARLY PERTURBED EQUATION WITH A TRIPLE ROOT OF THE DEGENERATE EQUATION

Qian Yang¹,
Mingkang Ni^2,3, ,

1.
College of Science, University of Shanghai for Science and Technology, 200093 Shanghai, China
2.
School of Mathematical Sciences, East China Normal University, No.500 Dongchuan Rd, 200241 Shanghai, China
3.
Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, No. 500 Dongchuan Rd, 200241 Shanghai, China

Corresponding author: Email: xiaovikdo@163.com(M. Ni)
Fund Project: The authors were supported by National Natural Science Foundation of China (No. 11871217) and the Science and Technology Commission of Shanghai Municipality (No. 18dz2271000)

Abstract

Abstract

A singularly perturbed boundary value problem for a stationary equation of reaction-diffusion type in the case when reactive term undergoes discontinuity along some curve that is independent of the small parameter is studied. This is a new class of problems with triple roots of the degenerate equation, which leads to the formation of complex multizonal internal layers in the neighborhood of the discontinuity curve. By the method of asymptotic differential inequalities and matching asymptotic expansion, the existence of a contrast structure solution is proved. Using a different modified boundary layer function method, the asymptotic representation of point itself and this solution are constructed.
- Reaction-diffusion equation /
- multizonal internal layer /
- a triple root of the degenerate equation /
- discontinuous dynamical system
MSC: 35A21, 35B25, 35C20

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References

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