A Class of Right-Hand Discontinuous Singularly Perturbed Boundary Value Problems With Turning Points

SHUAI Xin; NI Mingkang

doi:10.21656/1000-0887.440353

Volume 45 Issue 4

Apr. 2024

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SHUAI Xin, NI Mingkang. A Class of Right-Hand Discontinuous Singularly Perturbed Boundary Value Problems With Turning Points[J]. Applied Mathematics and Mechanics, 2024, 45(4): 470-489. doi: 10.21656/1000-0887.440353

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A Class of Right-Hand Discontinuous Singularly Perturbed Boundary Value Problems With Turning Points

doi: 10.21656/1000-0887.440353

SHUAI Xin,
NI Mingkang^,

School of Mathematical Sciences, East China Normal University, Shanghai 200241, P.R.China

Received Date: 2023-12-11
Rev Recd Date: 2024-01-12
Publish Date: 2024-04-01

Abstract

Abstract

The asymptotic behavior of solutions to a class of right-hand discontinuous 2nd-order semilinear singularly perturbed boundary value problems with turning points was studied. Firstly, the original problem was divided into left and right problems at the discontinuity, the accuracy of the asymptotic solution to the left problem was improved through modification of the regularization equation for the left problem degradation problem, and the existence of the smooth solution to the left problem was proved by means of the Nagumo theorem. Secondly, the solution to the right problem was proved to have a spatial contrast structure, and the asymptotic solution to the original problem was obtained through smooth joints at the discontinuity points. Finally, the correctness of the results was verified by an example.
- singular perturbation,
- boundary value problem,
- turning point,
- discontinuous right-hand side,
- spatial contrast structure,
- asymptotic solution estimation

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References(18)

References

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