拟线性常微分方程组边值问题的奇摄动

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基金项目: 国家自然科学基金资助课题

Singular Perturbation of Boundary Value Problem of Systems for Quasilinear Ordinary Differential Equations

摘要: 本文研究拟线性常微分方程组边值问题x′=f(t,x,y,ε),εy″=g(t,x,y,ε)y′+h(t,x,y,ε), x(0,ε)=A(ε),y(0,ε)=B(ε),y(1,ε)=C(ε)的奇摄动.其中x,f,y,h,A,B和C均属于Rⁿ和g是对角矩阵.在适当的假设下,利用对角化技巧和微分不等式理论获得了解的存在和它的按分量逐个一致有效的估计.
- 拟线性系统 /
- 奇摄动边值问题 /
- 对角化和微分不等式 /
- 渐近展开
Abstract: In this paper, we study the singular perturbation of boundary value problem of systems for quasilinear ordinary differential equations: x′=f(t,x,y,ε),εy″=g(t,x,y,ε)y′+h(t,x,y,ε), x(0,ε)=A(ε),y(0,ε)=B(ε),y(1,ε)=C(ε) where x,f,y,h,A,B and C belong to Rⁿ and a is a diagonal matrix.Under the appropriate assumptions, using the technique of diagonalization and the theory of differential inequalities we obtain the existence of solution and its componentwise uniformly valid asymptotic estimation.
- quasilinear systems /
- singularly perturbed boundary value problem /
- diagonalization and differential inequality /
- asymptotic expansion

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