Singularly perturbed solution for weakly nonlinear equations with two parameters
陈丽华;莫嘉琪
2007, 28(10):
1343-1348 .
doi:10.1007/s10483-007-1007-y
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A class of singularly perturbed boundary value problems of weakly nonlinear equation for fourth order on the interval [a, b] with two parameters is considered. Under suitable conditions, firstly, the reduced solution and formal outer solution are constructed 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 transformation 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 interval [a, b] and asymptotic behavior of solution for the original boundary value problem are proved. Satisfying results are obtained.
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