Answer: Find the temperature in Prob. 13 with L 11. C = 1,
Chapter 12, Problem 12.1.90(choose chapter or problem)
Consider \(v_{t}=c^{2} v_{x x}-v \quad(0<x<L, t>0)\), \(v(0, t)=0, v(L, t)=0, v(x, 0)=f(x)\), where the term -v models heat transfer to the surrounding medium kept at temperature 0. Reduce this PDE by setting v(x, t)= u(x, t)w(t) with w such that u is given by (9), (10).
Text Transcription:
v_t=c^2v_xx - v(0 < x < L, t > 0)
v(0, t)=0, v(L,t)=0, v(x,0)=f(x)
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