Singularly perturbed solution for weakly nonlinear equations with two parameters |
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Authors: | Chen Li-hua Mo Jia-qi |
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Institution: | Department of Mathematics and Computer Science, Fuqing Branch of Fujian Normal University, Fuqing 350300, Fujian Province, P. R. China;Division of Computational Science, E-Institutes of Shanghai Universities at SJTU, Shanghai 200240, P. R. China;Department of Mathematics, Huzhou Teachers College, Huzhou 313000, Zhejiang Province, P. R. China |
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Abstract: | A class of singularly perturbed boundary value problems of weakly non- linear equation for fourth order on the intervala,b]with two parameters is considered. Under suitable conditions,firstly,the reduced solution and formal outer solution are con- structed using the expansion method of power series.Secondly,using the transformation of stretched variable,the first boundary layer corrective term near x=a is constructed which possesses exponential attenuation behavior.Then,using the stronger transfor- mation of stretched variable,the second boundary layer corrective term near x=a is constructed,which also possesses exponential attenuation behavior.The thickness of second boundary layer is smaller than the first one and forms a cover layer near x=a. Finally,using the theory of differential inequalities,the existence,uniform validity in the whole intervala,b]and asymptotic behavior of solution for the original boundary value problem are proved.Satisfying results are obtained. |
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Keywords: | nonlinear two parameters singular perturbation |
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