MIXED BOUNDARY VALUE PROBLEM FOR SECOND-ORDER SYSTEM OF DIFFERENTIAL EQUATIONS OF THE ELLIPTIC TYPE

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MIXED BOUNDARY VALUE PROBLEM FOR SECOND-ORDER SYSTEM OF DIFFERENTIAL EQUATIONS OF THE ELLIPTIC TYPE

MIXED BOUNDARY VALUE PROBLEM FOR SECOND-ORDER SYSTEM OF DIFFERENTIAL EQUATIONS OF THE ELLIPTIC TYPE

MIXED BOUNDARY VALUE PROBLEM FOR SECOND-ORDER SYSTEM OF DIFFERENTIAL EQUATIONS OF THE ELLIPTIC TYPE

MIXED BOUNDARY VALUE PROBLEM FOR SECOND-ORDER SYSTEM OF DIFFERENTIAL EQUATIONS OF THE ELLIPTIC TYPE

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数学物理学报(英文版) ›› 1995, Vol. 15 ›› Issue (1): 58-64.

陈庆祥

Dept. of Math., Zhongshan University, Gangzhou 510275, China

收稿日期:1991-07-25 修回日期:1993-03-22 出版日期:1995-03-25 发布日期:1995-03-25

Chen Qingxiang

Dept. of Math., Zhongshan University, Gangzhou 510275, China

Received:1991-07-25 Revised:1993-03-22 Online:1995-03-25 Published:1995-03-25

摘要： In this paper.the following mixed boundary value problem for second-order system of differential equations of the elliptic type will be discussed to find the function u and v such that they satisfy:
[(¹₀⁰_λ)(∂²)/(∂x²)+(_λ-1⁰₀^λ-1)(∂²)/(∂x∂y)+(^λ₀¹₀(∂²)/(∂y²)](_v^u)
+(_d₂₁(x,y)^d₁₁(x,y)_d₂₂(x,y)^d₁₂(x,y))[¹₀⁰₁(∂/∂x)+(⁰₁^-1₀)(∂/∂y)](_v^u)=(_f₂^f₁)(1)
u|c=g(z),(2)
Σ^-1f_c((∂u)/(∂y)+(∂v)/(∂x))δ(s)ds=k₁,(7')
v(z_η)=k₂,(13)
The solution of this problem is found by means of the theory of generalized analytic function and the integral equation method for solving boundary value problems.

关键词: elliptic type, differential eguation, boundary value problem

Abstract: In this paper.the following mixed boundary value problem for second-order system of differential equations of the elliptic type will be discussed to find the function u and v such that they satisfy:
[(¹₀⁰_λ)(∂²)/(∂x²)+(_λ-1⁰₀^λ-1)(∂²)/(∂x∂y)+(^λ₀¹₀(∂²)/(∂y²)](_v^u)
+(_d₂₁(x,y)^d₁₁(x,y)_d₂₂(x,y)^d₁₂(x,y))[¹₀⁰₁(∂/∂x)+(⁰₁^-1₀)(∂/∂y)](_v^u)=(_f₂^f₁)(1)
u|c=g(z),(2)
Σ^-1f_c((∂u)/(∂y)+(∂v)/(∂x))δ(s)ds=k₁,(7')
v(z_η)=k₂,(13)
The solution of this problem is found by means of the theory of generalized analytic function and the integral equation method for solving boundary value problems.

Key words: elliptic type, differential eguation, boundary value problem

陈庆祥. MIXED BOUNDARY VALUE PROBLEM FOR SECOND-ORDER SYSTEM OF DIFFERENTIAL EQUATIONS OF THE ELLIPTIC TYPE[J]. 数学物理学报(英文版), 1995, 15(1): 58-64.

Chen Qingxiang. MIXED BOUNDARY VALUE PROBLEM FOR SECOND-ORDER SYSTEM OF DIFFERENTIAL EQUATIONS OF THE ELLIPTIC TYPE[J]. Acta mathematica scientia,Series B, 1995, 15(1): 58-64.

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