ôu a?u Let u be the unique solution of where (x, t) e (0, 1) x (0, 0), u(x, 0) = %3D sin Tx, x e (0, 1) u(0, t) = u(1, t) = 0t e (0, 0) Then which of the following are true? (a) 3 (x, t) e (0, 1) × (0, o) s.t. u(x, t) = 0 ди (x,1) =0 ốt (b) 3 (x, t) e (0, 1) x (0, c0) s.t. (c) The function e'u(x, t) is bounded for (x, t) e (0, 1) x (0, 0)
ôu a?u Let u be the unique solution of where (x, t) e (0, 1) x (0, 0), u(x, 0) = %3D sin Tx, x e (0, 1) u(0, t) = u(1, t) = 0t e (0, 0) Then which of the following are true? (a) 3 (x, t) e (0, 1) × (0, o) s.t. u(x, t) = 0 ди (x,1) =0 ốt (b) 3 (x, t) e (0, 1) x (0, c0) s.t. (c) The function e'u(x, t) is bounded for (x, t) e (0, 1) x (0, 0)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
solve correct both, handwritten
Transcribed Image Text:If u(x, t) is a solution of u, = uxx
* u(x, 0) = 1+ x+ sin (ax) cos (Tx)
u(0, t) = 1, u(1, t) = 2. Then
0 <x<1
t>0
(a) u
2 4
3
3
(b) u
4 4
1
-37?
+-e
4 2
1
--472
(c) u
(e)
(d) и
4
+-e
4
Transcribed Image Text:ôu a?u
Let u be the unique solution of
where (x, t) e (0, 1) x (0, 0), u(x, 0) =
sin Tx, x e (0, 1) u(0, t) = u(1, t) 0t e (0, 0) Then which of the following are true?
!!
(a) 3 (x, t) e (0, 1) x (0, 0) s.t. u(x, t) = 0
(b) 3 (x, t) e (0, 1) x (0, o) s.t.
ди
(x,()%3D0
(c) The function e'u(x, t) is bounded for (x, t) e (0, 1) × (0, 0)
(d) 3 (x, t) e (0, 1) x(0, 0) s.t. u(x, t) > 1
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