1. Consider the periodic heat equation U₁ = UII' 00 u (0,t) =u (2n,t), ur (0,t) = u(2n,t),t>0 u (x,0) = f(x), 0
1. Consider the periodic heat equation U₁ = UII' 00 u (0,t) =u (2n,t), ur (0,t) = u(2n,t),t>0 u (x,0) = f(x), 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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Transcribed Image Text:1. Consider the periodic heat equation
U₁ = UII'
u (0, t) = u (2n, t),
u (x,0) = f(x),
0<x<2π, t> 0
ur (0,t) = uz (2π, t), t> 0
0<x< 2π
where f(x) is any smooth periodic function. This system describes the heat evolu-
tion on a circular insulated wire of length 27.
(a) Find a (formal) solution to the above boundary value problem.
(b) Find limou (x, t) for all 0 < x < 27, and explain the physical interpretation
of your result.
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