奇摄动拟线性系统的边界层和角层性质
Boundary and Angular Layer Behavior in Singular Perturbed Quasilinear Systems
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摘要: 本文利用微分不等式的方法研究二阶拟线性系统狄立克雷问题解的存在和当ε→0+时它们的渐近性质.根据退化解在(a,b)中是否有连续的一阶偏导数,研究了解的两种渐近形式,从而导出边界层和角层现象.Abstract: In this paper,using the method of differential inequalities,we study the existence of solutions and their asymptotic behavior,as ε→0+ of Dirichlet problem for a second order quasilinear systems Denendine on whether the reduced solution u(t) has or does not have a continuous first-derivative in(a,b),we study two types of asymptotic behavior,thus leading to the phenomena of boundary and angular layers.
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[1] O'Donnell,M,A.,Boundary and comer layer behavior in semilinear systems of boundary value problems,SIAM J,Math.Anal.,2(1984). [2] Bernfeld,S. and V. Lakshmikantham,An Iniroduciion to Non-linear Boundary Value Problems,Academic Press,New York(1974). [3] Hebets,P,and M,Laloy,E'tude de problemes aux limites par la method des sur-et sous-solutions,Lecture Notes,Catholic University of Louvain(1974). -
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