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### Text of Równanie struny - mini.pw.edu.pl szaniawskaa/www/?download=rrc_z3.pdf · Równanie struny 1....

RRC, Zestaw 3, A.Sz.

Rwnanie struny

1.1.

utt 9uxx = sinx x R, t > 0u(x, 0) = cos x x Rut(x, 0) = 2xex

2x R

1.2.

utt 4uxx = 0 x (0, 4), t > 0u(0, t) = u(4, t) = 0 t 0u(x, 0) = 2 sin(x) 5 sin(3x) x 0, 4ut(x, 0) = 3 sin(2x) x 0, 4

1.3.

utt 8uxx = 0 x (0, 2), t > 0u(0, t) = u(2, t) = 0 t 0u(x, 0) = 0 x 0, 2

ut(x, 0) =

x dla x 0, 2 x dla x (, 2

1.4.

utt 4uxx = 2 sin(3t) x (0, 2 ), t > 0u(0, t) = u(2 , t) = 0 t 0u(x, 0) = 2x2 x x 0, 2 ut(x, 0) = 0 x 0, 2

1.5.

utt 4uxx = 2 sin(3x) x (0, 2 ), t > 0u(0, t) = u(2 , t) = 0 t 0u(x, 0) = 0 x 0, 2 ut(x, 0) = 2x2 x x 0, 2

1.6.

utt 4uxx = et(x3 x2) x (0, 1), t > 0u(x, 0) = x ut(x, 0) = x x 0, 1u(0, t) = 0 u(1, t) = et t 0

1.7.

utt 16uxx = 0 x (0, 2), t > 0u(0, t) = et u(2, t) = 3et t 0u(x, 0) = x2 x+ 1 x 0, 2

ut(x, 0) =

2x 1 dla x 0, 13 dla x (1, 2

1.8.

utt 4uxx = ( x) cos t x (0, ), t > 0u(x, 0) = x2 x+ x+ 1 ut(x, 0) = 3 sin 4x x 0, u(0, t) = 1 u(, t) = 1 + cos t t 0

1

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