Find all solutions of the one-dimensional heat equation

Chapter , Problem 24AAE

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Find all solutions of the one-dimensional heat equation that have the form \(w=e^{r t} \sin k x\) and satisfy the conditions that \(\mathrm{w}(0, \ \mathrm{t})=0\) and \(\mathrm{w}(\mathrm{L}, \ \mathrm{t})=0\). What happens to these solutions as \(\mathrm{t} \rightarrow \infty\)?

Equation Transcription:

Text Transcription:

w=e_rt sin kx

w(0,t)=0

w(L,t)=0

t right arrow infinity

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