kontsyslos070525

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

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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) +...
View Full Document

## This note was uploaded on 10/07/2011 for the course FMA 021 taught by Professor Pellepettersson during the Spring '11 term at Lund.

### Page1 / 4

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online