| 一类椭圆型方程Dirichlet外问题的奇摄动 |
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| 引用本文： | 谢峰.一类椭圆型方程Dirichlet外问题的奇摄动[J].数学季刊,2003,18(1):1-6. |
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| 作者姓名： | 谢峰 |
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| 作者单位： | Department of Applied Mathematics，Shanghai Jiaotong University，Shanghai 200030，China |
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| 基金项目： | SupportedbytheNationalScienceFoundationofChina(10 0 710 4 8) |
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| 摘 要： | § 1 . IntroductionSingularperturbationofDirichletproblemsforellipticequationswerediscussedbysomeauthors1 ] -4] ,butmostofwhathavebeenconsideredareboundeddomain .InthispapertheauthorconsiderDirichletexteriorproblemsasfollow :εL1 u]+L2 u]=f(x ,u ,ε) ,x∈Rn -Ω , ( 1)u(x) =g(x ,ε) ,x∈ Ω ,( 2 )whereL1 issecondorderellipticoperator:L1 u]=∑ni,j=1aij(x) 2 u xi xj+∑ni=1ai(x) u xi +a(x ,u) ,∑ni,j=1aijζiζj ≥δ0 >0 ,x∈Rn -Ω , ζ∈Rn ,ζ≠ 0 ,L2 isfirstorderdifferentialopera…
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| 关 键 词： | Dirichlet外问题 椭圆方程 奇异扰动 微分算子 形式渐进解 一致有效性 |
Singular Perturbation of a Class of Dirichlet Exterior Problems for Elliptic Equations |
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| XIE Feng.Singular Perturbation of a Class of Dirichlet Exterior Problems for Elliptic Equations[J].Chinese Quarterly Journal of Mathematics,2003,18(1):1-6. |
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| Authors: | XIE Feng |
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| Institution: | DepartmentofAppliedMathematics,ShanghaiJiaotongUniversity,Shanghai200030,China |
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| Abstract: | In this paper,we consider a class of singularly perturbed Dirichlet exterior problems for ellip-tic equations.Under the appropriate conditions we construct the formally asymptotic solution of the problem described.Using differential inequaltiy theory we prove the existence of the solution of original problem and the uniforly validity of the formal solution. |
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| Keywords: | singular perturbation elliptic equation differential inequality |
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