Singularly Perturbed Soluton for Weakly Nonlinear Equations With Two Parameters

CHEN Li-hua; MO Jia-qi

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CHEN Li-hua, MO Jia-qi. Singularly Perturbed Soluton for Weakly Nonlinear Equations With Two Parameters[J]. Applied Mathematics and Mechanics, 2007, 28(10): 1197-1202.

Citation:

CHEN Li-hua, MO Jia-qi. Singularly Perturbed Soluton for Weakly Nonlinear Equations With Two Parameters[J]. Applied Mathematics and Mechanics, 2007, 28(10): 1197-1202.

Citation:

CHEN Li-hua, MO Jia-qi. Singularly Perturbed Soluton for Weakly Nonlinear Equations With Two Parameters[J]. Applied Mathematics and Mechanics, 2007, 28(10): 1197-1202.

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Singularly Perturbed Soluton for Weakly Nonlinear Equations With Two Parameters

CHEN Li-hua¹,
MO Jia-qi^2,3

1.
Department of Mathematics and Computer Science, Fuqing Branch of Fujian Normal University, Fuqing, Fujian 350300, P. R. China;

Received Date: 2007-01-16
Rev Recd Date: 2007-08-08
Publish Date: 2007-10-15

Abstract

Abstract

A class of singularly perturbed boundary value problem of weakly nonlinear equation for fourth order on the finite interval with two parameters is considered.Under suitable conditions,firstly,using the expansion method of power series,the reduced solution and formal outer solution are constructed.Secondly,using the transformation of stretched variable,the first boundary layer corrective term near the left endpoint is constructed which possesses exponential attenuation behavior.And then,using the stronger transformation of stretched variable,the second boundary layer corrective term near the left endpoint is constructed too,which also possesses exponential attenuation behavior.The thickness of second boundary layer smaller than first boundary layer and forms the cover layer near the left endpoint.Finally,using the theory of differential inequalities the existence,uniform validity in the whole interval and asymptotic behavior of solution for the original boundary value problem are proved.The satisfying results are obtained.
- nonlinear,
- two parameters,
- singular perturbation

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References(16)

References

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