tailieunhanh - Handbook of mathematics for engineers and scienteists part 190

Handbook of mathematics for engineers and scienteists part 190. Tài liệu toán học quốc tế để phục vụ cho các bạn tham khảo, tài liệu bằng tiếng anh rất hữu ích cho mọi người. | . Elliptic Equations 1291 . Domain -œ x œ 0 y œ. Second boundary value problem. A half-plane is considered. A boundary condition is prescribed dy w f x at y 0. Solution w x y - Î f t G x y t 0 dt Î i n G x y t n d dy. J -œ J 0 J -œ 1 . The Green s function for A -s2 0 G x y n 2n K0 sQi K s 2 Qi V x - t 2 y - n 2 Q2 V x - t 2 y n 2 2 . The Green s function for A k2 0 G x y n - 4 H0 kQi H02 kp2 . Remark. The radiation Sommerfeld conditions at infinity were used to obtain the solution with À 0 see Tikhonov and Samarskii 1990 and Polyanin 2002 . . Domain 0 x œ 0 y œ. First boundary value problem. A quadrant of the plane is considered. Boundary conditions are prescribed w f1 y at x 0 w f2 x at y 0. Solution Î fi n dG x y t n J0 dt. . 0 œ w x y t n G x y t n dtdn. 00 dn îœ fM 0 d G x y t n on d 1 . The Green s function for A -s 2 0 G x y n 2n Ko spi - Ko sQ2 - Ko sq3 Ko s 4 Qi V x - S 2 y - n 2 Q2 V x - S 2 y n 2 Q3 x S 2 y - n 2 Q4 V x S 2 y n 2. 2 . The Green s function for A k2 0 U 2 U 2 u 2 U 2 7z G x y S n -4 _H0 ky1 - Ho ky2 - Ho ky3 Ho kP4 . 1292 Linear Equations and Problems of Mathematical Physics . Domain 0 x œ 0 y œ. Second boundary value problem. A quadrant of the plane is considered. Boundary conditions are prescribed dx w fi y at x 0 dy w f2 x at y 0. Solution w x y - r fi y G x y 0 y n - f2 G x y t 0 d Jo Jo f f n G x y t n dtdy. Jo Jo 1 . The Green s function for A -s2 0 G x y t y 2n Ko sQi Ko SQ2 Ko spa Ko sp4 pi V x -1 2 y - y 2 P3 V x 1 2 y - y 2 2 . The Green s function for A k2 o - . - . - . - . G x y s y -4 Ho kQ1 Ho ky2 Ho ky3 Ho ky4b . P2 x - 02 y n 2 P4 x 02 y n 2. . Domain 0 x a 0 y b. First boundary value problem. A rectangle is considered. Boundary conditions are prescribed w fi y at x 0 w fß x at y 0 w f2 y at x a w f4 x at y b. 1 . Eigenvalues of the homogeneous problem with o it is convenient to label them with a double subscript 22 Anm V2 m i a2 b2 n 1 2 . m 1 2 . Eigenfunctions and the norm squared wnm

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