kontsyslos070525

kontsyslos070525 - DEAÖGA AEA ÖGA EGAYE5Ô 755 a Ód e...

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Unformatted text preview: DEAÖGA AEA ÖGA EGAYE5Ô 755 a Ód e ÐÐ ∂ 2 u ∂t 2 − ∂ 2 u ∂x 2 = 0 , x > , t > u (0 , t ) = 0 , t > u ( x, 0) = 0 , x > u t ( x, 0) = h ( x ) , x > b Ø u − Úa ÖaeÒÙdda fÓ ÖØ×ØØÒ iÒgaÚ u Ñ edaÚ ×eeÒd eÔ x Ø iÐÐh e Ða R D g ÐÐeÖ ∂ 2 u − ∂t 2 − ∂ 2 u − ∂x 2 = 0 , x ∈ R , t > u − ( x, 0) = 0 , x ∈ R u − t ( x, 0) = h − ( x ) , x ∈ R d Ö h − Öd eÒÙdda fÓ ÖØ×ØØÒ iÒg eÒaÚ h E Ò Ðig ØdA ÐeÑ b eÖØ×fÓ ÖÑ e ÐÖd u ( x, t ) = u − ( x, t ) = 1 2 integraldisplay x + t x − t h − ( y ) dy ÓÑ x > , t > x − 2 y − 1 y = H ( x ) 9 x 5 y 5 49 y = u ( x, 3) Ø H Úa ÖaeÒÔ Ö iÑ iØ iÚ Ø iÐÐ h − Ðj H ( x ) = integraldisplay x −∞ h − ( y ) dy G Öa feÒ Ø iÐÐ H Ú i×a ×Ø iÐÐhög eÖ aÒÚÒda Öea ØÓ ÐkÒ iÒgaÚ iÒ Øeg Öa ÐeÖ E fØeÖ×ÓÑ u ( x, 3) = 1 2 ( H ( x + 3) − H ( x − 3)) kaÒÚ iÖ iØa u ( x, 3) g eÒÓÑ a ØØfö Ö×k jÙ Øa H ØÖe×ØegØÚÒ ×ØeÖÓh − H ØÖe ×ØegØhög eÖE fØeÖd iÚ i× iÓÒÑ ed fÖÚ ig Öa feÒ Ø iÐÐhög eÖ ×aÑÑ a ×ØØb ÐiÖ u (3 , t ) = 1 2 ( H (3 + t ) − H (3 − t )) E fØeÖ×ÓÑ H Ö jÑ ÒÖ H (3 − t ) = H ( t − 3) A ÐÐØ××eÖ u (3 , t ) Ù ØÔ ×aÑÑ a ×ØØ×ÓÑ u ( x, 3) Ód e ÐÐ u t − u xx = 0 , x > , t > u x (0 , t ) = 0 , t > u ( x, 0) = cos x, x > aÒdÚ iÐÐkÓ ÖeØÖeØØhÓÑ Óg eÒ ØeÙÑ aÒÒÚ iÐÐkÓ Öigö Öd Ö fö ÖeÒ jÑ Ò fÓ ÖØ×ØØÒ iÒgaÚ u ed aÚ ×eeÒd eÔ x a ÐÐad eÒ u + D g ÐÐeÖ braceleftbigg u + t − u + xx = 0 , x ∈ R , t > u + ( x, 0) = cos x, x ∈ R F ÓÙ Ö ieÖØÖaÒ × fÓ ÖÑ eÖaÒÙÑ edaÚ ×eeÒd eÔ x ØØ U ( ξ, t ) = integraldisplay ∞ −∞ e − iξx u + ( x, t ) dx D g ÐÐeÖ U t + ξ 2 U = 0 ⇔ U ( ξ, t ) = c ( ξ ) e − ξ 2 t D t = 0 fÖÚ ia ØØ c ( ξ ) = F (cos)( ξ ) = π ( δ ( ξ + 1) + δ ( ξ − 1)) A ÐÐØ×Ö U ( ξ, t ) = π ( δ ( ξ + 1) +...
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kontsyslos070525 - DEAÖGA AEA ÖGA EGAYE5Ô 755 a Ód e...

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