Solved: WRITING PROJECT. Wave and Heat Equations.Compare

Chapter 12, Problem 12.1.74

(choose chapter or problem)

(Arbitrary temperatures at ends) If the ends x = 0 and x = L of the bar in the text are kept at constant temperatures \(\boldsymbol{U}_{1}\) and \(\boldsymbol{U}_{2}\), respectively, what is the temperature \(u_{I}(x)\) in the bar after a long time (theoretically, as \(t \rightarrow \infty\))? First guess, then calculate.

\(\begin{array}{l} f(x)=x \text { if } 0<x<2.5, f(x)=2.5 \text { if } 2.5<x<7.5,\\ f(x)=10-x \text { if } 7.5<x<10 \end{array} \)

Text Transcription:

U_1

U_2

u_I(x)

t rightarrow infinity

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