A thin wire coinciding with the x-axis on the interval [-L, L] is bent into the shape of a circle so that the ends X=-Land x = Lare joined. Under certain conditions the temperature u(x, t) in the wire satisfies the boundary value problem. a²u ди dx at u(-L, t) = u(L, t), t>0 ди ди t>0 = -L 0, axlx=-L axx=L' u(x, 0) = f(x), -L
A thin wire coinciding with the x-axis on the interval [-L, L] is bent into the shape of a circle so that the ends X=-Land x = Lare joined. Under certain conditions the temperature u(x, t) in the wire satisfies the boundary value problem. a²u ди dx at u(-L, t) = u(L, t), t>0 ди ди t>0 = -L 0, axlx=-L axx=L' u(x, 0) = f(x), -L
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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![A thin wire coinciding with the x-axis on the interval [-L, L] is bent into the shape of a circle so that the ends
X=-Land x = Lare joined. Under certain conditions the temperature u(x, t) in the wire satisfies the boundary value
problem
²u du
dx at
u(-L, t) = u(L, t), t>0
ди
ди
=
-L<x<L, 1 > 0,
t>0
axlx=-L axx=L'
u(x, 0) = f(x), -L<x<L.
Find the temperature u(x, t).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc5779d6d-aa05-4ad7-80c7-ed0d0a2afe0f%2F55dfdf7d-b488-437e-8f6e-4f85c06e00dc%2Fxm74tov_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A thin wire coinciding with the x-axis on the interval [-L, L] is bent into the shape of a circle so that the ends
X=-Land x = Lare joined. Under certain conditions the temperature u(x, t) in the wire satisfies the boundary value
problem
²u du
dx at
u(-L, t) = u(L, t), t>0
ди
ди
=
-L<x<L, 1 > 0,
t>0
axlx=-L axx=L'
u(x, 0) = f(x), -L<x<L.
Find the temperature u(x, t).
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