chpp22 - Theorem Note Theorem Note(x y 2u 2u 2u u u a 2 2b...

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线 线
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线 线
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, 讨论 了三 , 斯方 , , , , 圆型 .
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Theorem 两个 , 线 Note , 一些 , .
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Theorem 两个 , 线 Note , 一些 , .
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两个 ( x, y ) 线 形式 : a 2 u ∂x 2 + 2 b 2 u ∂x∂y + c 2 u ∂y 2 + d ∂u ∂x + e ∂u ∂y + fu + g = 0 , (1) a , b , c , d , e , f g x , y . . , a , b , c , 一个不 0, , 为二 .
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(cont.) ξ = φ ( x, y ) , η = ψ ( x, y ) . (2) 为了 ξ η , ( ξ, η ) ( x, y ) = 0 . (3) , A 2 u ∂ξ 2 + 2 B 2 u ∂ξ∂η + C 2 u ∂η 2 + D ∂u ∂ξ + E ∂u ∂η + Fu + G = 0 , (4)
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(cont.) , A = a ∂φ ∂x 2 + 2 b ∂φ ∂x ∂φ ∂y + c ∂φ ∂y 2 , B = a ∂φ ∂x ∂ψ ∂x + b ∂φ ∂x ∂ψ ∂y + ∂φ ∂y ∂ψ ∂x + c ∂φ ∂y ∂ψ ∂y , C = a ∂ψ ∂x 2 + 2 b ∂ψ ∂x ∂ψ ∂y + c ∂ψ ∂y 2 , ...
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(cont.) B 2 - AC = ∂φ ∂x ∂ψ ∂y - ∂φ ∂y ∂ψ ∂x 2 ( b 2 - ac ) = ( ξ, η ) ( x, y ) 2 ( b 2 - ac ) . (5) 为了书 便 , Φ ξ, η, u, ∂u ∂ξ , ∂u ∂η D ∂u ∂ξ + E ∂u ∂η + Fu + G, (6)
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(cont.) A 2 u ∂ξ 2 +2 B 2 u ∂ξ∂η + C 2 u ∂η 2 ξ, η, u, ∂u ∂ξ , ∂u ∂η = 0 .
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