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Solve the heat equation subject to these conditions. Show all the work: separation of variable, finding the eigenvalues, finding the eigenfunctions, and so on. with the boundary conditions and the initial condition ut 12uxx = 0, 00, uz (0, t) = 0, uz (π, t)=0, t≥ 0; u(x,0)=1+sin³ z. Evaluate lim u(x, t) for all 0 < x < 7 and explain the physical interpretation of your result.

Solve the heat equation subject to these conditions. Show all the work: separation of variable, finding the eigenvalues, finding the eigenfunctions, and so on. with the boundary conditions and the initial condition ut 12uxx = 0, 00, uz (0, t) = 0, uz (π, t)=0, t≥ 0; u(x,0)=1+sin³ z. Evaluate lim u(x, t) for all 0 < x < 7 and explain the physical interpretation of your result.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve the heat equation subject to these conditions. Show all the work: separation of variable, finding the eigenvalues, finding the eigenfunctions, and so on. with the boundary conditions and the initial condition Ut - 12uxx = uz (0, t) = 0, 0, 0<x<, t>0, uz (π, t) = 0, t≥ 0; - u(x,0) = 1+ sin³ x. I. Evaluate lim u(x, t) for all 0<x< and explain the physical interpretation of your result. 200
Transcribed Image Text:Solve the heat equation subject to these conditions. Show all the work: separation of variable, finding the eigenvalues, finding the eigenfunctions, and so on. with the boundary conditions and the initial condition Ut - 12uxx = uz (0, t) = 0, 0, 0<x<, t>0, uz (π, t) = 0, t≥ 0; - u(x,0) = 1+ sin³ x. I. Evaluate lim u(x, t) for all 0<x< and explain the physical interpretation of your result. 200
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