圆形区域中的稳定问题 平面极坐标中的方程与边界条件 0/au\102 r(ar)Tr2002 00<r<a =n=f() 10/an)102u r(O)+2a2 00<T<a =n=f() 是适定的定解问题吗?不是!
Dirichlet Problem of Laplace Eqn in Circular Region Helmholtz Eqn in Orthogonal Curvilinear . . . Well-posed Problem in Circular Region Solutions of Well-posed Problem in Circular Region /«¥½¯K ²¡4I¥§>.^ 1 r ∂ ∂r r ∂u ∂r + 1 r 2 ∂ 2u ∂φ2 = 0 0 < r < a u r=a = f(φ) ©Û 1 r ∂ ∂r r ∂u ∂r + 1 r 2 ∂ 2u ∂φ2 = 0 0 < r < a u r=a = f(φ) ´·½½)¯KíºØ´ C. S. Wu 1Êù ©lCþ{(o)
圆形区域中的稳定问题 分析 10/au102u 00<r<a arar/r2 882 uln=f(o) 并不完全等价于原来的定解问题 a2 +=0x2+y2< ax2 ay2
Dirichlet Problem of Laplace Eqn in Circular Region Helmholtz Eqn in Orthogonal Curvilinear . . . Well-posed Problem in Circular Region Solutions of Well-posed Problem in Circular Region /«¥½¯K ©Û 1 r ∂ ∂r r ∂u ∂r + 1 r 2 ∂ 2u ∂φ2 = 0 0 < r < a u r=a = f(φ) ¿Ø du5½)¯K ∂ 2u ∂x2 + ∂ 2u ∂y2 = 0 x 2 + y 2 < a2 u x 2+y 2=a 2 = f C. S. Wu 1Êù ©lCþ{(o)
圆形区域中的稳定问题 分析 第一,在数学上,原来定解问题的微分方程在圆 内处处成立
Dirichlet Problem of Laplace Eqn in Circular Region Helmholtz Eqn in Orthogonal Curvilinear . . . Well-posed Problem in Circular Region Solutions of Well-posed Problem in Circular Region /«¥½¯K ©Û 1§3êÆþ§5½)¯K©§3 S??¤á C. S. Wu 1Êù ©lCþ{(o)
圆形区域中的稳定问题 分析 第一,在数学上,原来定解问题的微分方程在圆 内处处成立;然而变换到平面极坐标后,方程在 区间的端点φ=0和=2π并不成立
Dirichlet Problem of Laplace Eqn in Circular Region Helmholtz Eqn in Orthogonal Curvilinear . . . Well-posed Problem in Circular Region Solutions of Well-posed Problem in Circular Region /«¥½¯K ©Û 1§3êÆþ§5½)¯K©§3 S??¤á¶, C²¡4I§§3 «mà: φ = 0Úφ = 2π¿Ø¤á C. S. Wu 1Êù ©lCþ{(o)
圆形区域中的稳定问题 分析 第一,在数学上,原来定解问题的微分方程在圆 内处处成立;然而变换到平面极坐标后,方程在 区间的端点φ=0和=2π并不成立 严格说,在平面极坐标中,自变量φ的变化范围 是[0,27
Dirichlet Problem of Laplace Eqn in Circular Region Helmholtz Eqn in Orthogonal Curvilinear . . . Well-posed Problem in Circular Region Solutions of Well-posed Problem in Circular Region /«¥½¯K ©Û 1§3êÆþ§5½)¯K©§3 S??¤á¶, C²¡4I§§3 «mà: φ = 0Úφ = 2π¿Ø¤á î`§3²¡4I¥§gCþφCz ´[0, 2π] C. S. Wu 1Êù ©lCþ{(o)