Solved: Find the temperature in Prob. 13 with L 11. C = 1,
Chapter 12, Problem 12.1.88(choose chapter or problem)
(Bar with heat generation) If heat is generated at a constant rate throughout a bar of length \(L=\pi\) with initial temperature f(x) and the ends at x = 0 and \(\pi\) are kept at temperature 0, the heat equation is \(u_{t}=c^{2} u_{x x}+H\) with constant H > 0. Solve this problem. Hint. Set \(u=v-H x(x-\pi) /\left(2 c^{2}\right)\).
Text Transcription:
L=pi
pi
u_t=c^2u_xx + H
u=v-Hx(x-pi)/(2c^2)
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