The Higher Order Approximation of Solution of Quasilinear Second Order Systems for Singular Perturbation |
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Authors: | Lin Zongchi |
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Affiliation: | Department of Mathematics, Fujian Normal University, Fuzhou, China. |
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Abstract: | In this paper, using the theory of invariant region, the author considers the existence and the asymptotic behavior of solution of vector second order quasi-linear boundary value problem: $epsilon y''=f(x,y,epsilon)y''+g(x,y,epsilon)$$y(0,epsilon)=A(epsilon),y(1,epsilon)=B(epsilon)$as the positive perturbation parameter e tends to zero, where y, g, A and B are vector-valued and f is a matrix function. Under the appropriate assumptions the author obtains, involving the boundary layer, uniformly valid asymptotic solution of higher order approximation. |
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