Boundary and Interior Layer Behavior for Singularly Perturbed Vector Problem

Zhang Xiang

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1990 > 11(11): 999-1005

Zhang Xiang. Boundary and Interior Layer Behavior for Singularly Perturbed Vector Problem[J]. Applied Mathematics and Mechanics, 1990, 11(11): 999-1005.

Citation:

Zhang Xiang. Boundary and Interior Layer Behavior for Singularly Perturbed Vector Problem[J]. Applied Mathematics and Mechanics, 1990, 11(11): 999-1005.

Citation:

Zhang Xiang. Boundary and Interior Layer Behavior for Singularly Perturbed Vector Problem[J]. Applied Mathematics and Mechanics, 1990, 11(11): 999-1005.

PDF( 432 KB)

Boundary and Interior Layer Behavior for Singularly Perturbed Vector Problem

Zhang Xiang

Anhui Normal University, Wuhu

Received Date: 1988-12-12
Publish Date: 1990-11-15

Abstract

Abstract

In this paper, we consider the vector nonlinear boundary value problem:εy″=f(x,y,z,y',ε), y(0)=A₁ y(1)=B₁ εz″=f(x,y,z,z',ε), z(0)=A₂ z(1)=B₂ where ε>0 is a small parameter,0≤x≤1 f and g are continuous functions in R⁴. Under appropriate assumptions, by means of the differential inequalities, we demonstrate the existence and estimation, involving boundary and interior layers, of the solutions to the above problem.
- singular perturbation,
- differential inequality,
- boundary layer,
- inner layer

FullText(HTML)

References(9)

References

[1]	莫嘉琪,用微分不等式对二阶拟线性方程奇摄动解的估计,数学研究与评论,.(1988), 86-91.
[2]	Hooves.F. A., Effective characterization of the asymptotic behavior of solutions of singularly perturbed boundary value problem, SIAM. J. Appl. Mcrth.,30,(1976), 296-305.
[3]	Hooves, F.A., Differential inequalities of higher order and the asymptotic solution of nonlinear boundary value problems. SIAM. J. Math:. Anal., 13, 1(1982),6l-82.
[4]	Lin Zhong-chi(林宗池), Sorne estimations of solution of nonlinear boundary value problem for second order systems, 数学物理学报,7, 2 (1987), 229-259.
[5]	Lin Zhong-chi(林宗池), The higher order approximation of solution of quasilinear second order systems for singular perturbation, Chin. Ann. of Math., 8B, 3(1987), 357-363.
[6]	Chang, G. W., Diagonalization method for a vector boundary value problem of singular perturbation type, J. Math. Anal. Appl.,48(1974), 652-665.
[7]	Kelley, W.G.Existence and uniqueness of solutions for vector problems containing small parameters. J. Math. Anal. 4pp1.,131(1988), 295-312
[8]	Lan, Chin-chin, Boundary value problem for second and third order differential equations,.J. Diff.Equs, 18, 2(1975), 258-274.
[9]	刘光旭,关于奇摄动拟线性系统,应用数学和力学,8 1 (1987), 987-978.