| 椭圆型Boussinesq方程Dirichlet问题解的存在性和唯一性 |
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| 引用本文： | 李海龙.椭圆型Boussinesq方程Dirichlet问题解的存在性和唯一性[J].鞍山师范学院学报,2003,5(6):8-17. |
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| 作者姓名： | 李海龙 |
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| 作者单位： | 鞍山师范学院,数学系,辽宁,鞍山,114005 |
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| 摘 要： | 在关于k,hb,μb的非常弱的假设条件下,在Sobolev空间中证明了非齐次Dirichlet边界条件u=ud(x,y), (x,y)∈(e)Ω下非齐次椭圆型Boussinesq方程-（△）*(K(x,y)(u-hb)（△）u)=f(x,y,u), (x,y)∈Ω的解的唯一性以及齐次椭圆型Boussinesq方程（△）*(K(x,y)(u-hb)（△）u)=0, (x,y)∈Ω的解的存在性,其中Ω为有界多边形域.并给出反例,指出对一给定的f(x,y),非齐次方程-（△）*(K(x,y)(u-hb)（△）u)=f(x,y,u), (x,y)∈Ω的Dirichlet问题是不可解的.
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| 关 键 词： | 椭圆型Boussinesq方程 Dirichlet问题 Sobolev空间 唯一性 存在性 有限元法 |
On existence and uniqueness of solution to Dirichlet problem of elliptic Boussinesq equation |
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| Abstract.On existence and uniqueness of solution to Dirichlet problem of elliptic Boussinesq equation[J].Journal of Anshan Teachers College,2003,5(6):8-17. |
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| Authors: | Abstract |
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| Abstract: | The uniqueness of the solution to the nonhomogeneous elliptic Boussinesq equation-（△）*(K(x,y)(u-hb)（△）u)=f(x,y,u), (x,y)∈Ω(1)with nonhomogeneous Dirichlet boundary conditionu=ud(x,y), (x,y)∈(e)Ω,(2)and the existence of the solution to the honogeneous elliptic Boussinesq equation（△）*(K(x,y)(u-hb)（△）u)=0, (x,y)∈Ω(3)with the same Dirichlet boundary condition (2) are proved in the Sobolev space H1(Ω) for a bounded polygon domain Ω under very weak assumptions about K,hb and ud.Counter example is given to show that the Dirichlet problem of the nonhomogeneous equation (1) may be insolvable for a certain f(x,y). |
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| Keywords: | Elliptic Boussinesq equation Finite element method M matrix |
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