69. (a) Use the Laplace transform to solve the heat conduction problem Ut = KUxx, 0 0, и (х, 0) — 0, г > 0, u (0, t) = f (t), u (x, t) → 0 as x → 0, t> 0. (b) Derive Duhamel's formula и (х, t) f (t –...

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69. (a) Use the Laplace transform to solve the heat conduction problem<br>Ut = KUxx,<br>0 < x < ∞,<br>t > 0,<br>и (х, 0) — 0, г > 0,<br>u (0, t) = f (t), u (x, t) → 0 as<br>x → 0,<br>t> 0.<br>(b) Derive Duhamel's formula<br>и (х, t)<br>f (t – T)<br>duo<br>dт,<br>where<br>).<br>Juo<br>x2<br>exp<br>dt<br>V4TK<br>4kt<br>

Extracted text: 69. (a) Use the Laplace transform to solve the heat conduction problem Ut = KUxx, 0 < x="">< ∞,="" t=""> 0, и (х, 0) — 0, г > 0, u (0, t) = f (t), u (x, t) → 0 as x → 0, t> 0. (b) Derive Duhamel's formula и (х, t) f (t – T) duo dт, where ). Juo x2 exp dt V4TK 4kt

Jun 05, 2022

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69. (a) Use the Laplace transform to solve the heat conduction problem Ut = KUxx, 0 0, и (х, 0) — 0, г > 0, u (0, t) = f (t), u (x, t) → 0 as x → 0, t> 0. (b) Derive Duhamel's formula и (х, t) f (t –...

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