Consider the following initial-boundary value problem: 8²u du Pu +3 = 4- -8 Ət² Ət Əx² u(0, t) = 2, u(1, t) = 4 u(x,0)=2-1+31², (DE) (BC), (IC1), (IC2), ди Ət 0 0, t> 0, 0 < x < 1, (1,0) = 3x - 1₁ 0
Consider the following initial-boundary value problem: 8²u du Pu +3 = 4- -8 Ət² Ət Əx² u(0, t) = 2, u(1, t) = 4 u(x,0)=2-1+31², (DE) (BC), (IC1), (IC2), ди Ət 0 0, t> 0, 0 < x < 1, (1,0) = 3x - 1₁ 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Need A and B
Transcribed Image Text:Consider the following initial-boundary value problem:
8²u du
+3-
Ət² Ət
u(0, t) = 2,
u(1,0)=2-1+31²,
(DE)
(BC),
(IC1),
(IC2),
Ju
Ət
Fu
-8
Əx²
u(1, t) = 4
= 4-
0 << 1,t> 0,
t> 0,
0 < x < 1,
(1,0) = 3x - 1₁
0<< 1.
(a) Find a steady-state solution v(z); i.e., a time-independent function satisfying the differential
equation and the boundary conditions.
(b) Let v(z) be the steady state obtained in Part (a) and define w(z, t) = u(z,t)-(2), Write
down the initial-boundary value problem satisfied by w(z,t).
differential
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