Consider the inhomogeneous wave equation - c?uxx = f (x,t), Utt - where 1 ifx > 0, if x < 0. f(x, t) = (a) Consider the zero initial condition u(x,0) = 0, u¡ (x,0) = 0 for all x e R. On which domain (of (x, t)) does the solution vanish? (b) Consider the same equation but with initial condition |1 х<-1, и (х,0): U; (x, 0) = 0 for all x, 0 x> 1, on which domain does u vanish?
Consider the inhomogeneous wave equation - c?uxx = f (x,t), Utt - where 1 ifx > 0, if x < 0. f(x, t) = (a) Consider the zero initial condition u(x,0) = 0, u¡ (x,0) = 0 for all x e R. On which domain (of (x, t)) does the solution vanish? (b) Consider the same equation but with initial condition |1 х<-1, и (х,0): U; (x, 0) = 0 for all x, 0 x> 1, on which domain does u vanish?
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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Please answer a and b in detail.
Thank you!
Transcribed Image Text:Consider the inhomogeneous wave equation
c²uxx = f (x,t),
Utt
хх
where
if x > 0,
1
f (x, t) =
if x < 0.
(a)
Consider the zero initial condition u (x, 0) = 0, u¡ (x,0) = 0 for all x e R. On which
%3D
%3D
domain (of (x, t)) does the solution vanish?
(b)
Consider the same equation but with initial condition
1 x < -1,
u(x,0) =
и (х, 0) — 0 for all x,
0 x> 1,
on which domain does u vanish?
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