Solve the heat equation subject to these conditions. Show all the work: separation of variable, finding the eigenvalues, finding the eigenfunctions, and so on. u – 12uzx = 0, e0< x < #, t>0,with the boundary conditionsUz (0, t) = 0,Uz (T , t) = 0, t>0;and the initial conditionu(x,0) = 1 + sin x.Evaluate lim u(x,t) for all 0 < x < n and explain the physical interpretation of your result.

As per the question, we will solve by separation of the variable method.

u – 12uzx = 0, e0< x < #, t>0, with the boundary conditions Uz (0, t) = 0, Uz (T , t) = 0, t>0; and the initial condition u(x,0) = 1 + sin x. Evaluate lim u(x,t) for all 0 < x < n and explain the physical interpretation of your result.

u – 12uzx = 0, e0< x < #, t>0, with the boundary conditions Uz (0, t) = 0, Uz (T , t) = 0, t>0; and the initial condition u(x,0) = 1 + sin x. Evaluate lim u(x,t) for all 0 < x < n and explain the physical interpretation of your result.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 12T

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Question

Solve the heat equation subject to these conditions. Show all the work: separation of variable, finding the eigenvalues, finding the eigenfunctions, and so on.

u – 12uzx = 0, e0< x < #, t>0,
with the boundary conditions
Uz (0, t) = 0,
Uz (T , t) = 0, t>0;
and the initial condition
u(x,0) = 1 + sin x.
Evaluate lim u(x,t) for all 0 < x < n and explain the physical interpretation of your result.

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