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# Consider u t = k 2u x2 u. This corresponds to a one-dimensional rod either with heat ISBN: 9780321797056 284

## Solution for problem 2.3.8 Chapter 2.3

Applied Partial Differential Equations with Fourier Series and Boundary Value Problems | 5th Edition

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Problem 2.3.8

Consider u t = k 2u x2 u. This corresponds to a one-dimensional rod either with heat loss through the lateral sides with outside temperature 0 ( > 0, see Exercise 1.2.4) or with insulated lateral sides with a heat sink proportional to the temperature. Suppose that the boundary conditions are u(0, t) = 0 and u(L, t)=0. (a) What are the possible equilibrium temperature distributions if > 0? (b) Solve the time-dependent problem [u(x, 0) = f(x)] if > 0. Analyze the temperature for large time (t ) and compare to part (a).

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##### ISBN: 9780321797056

This textbook survival guide was created for the textbook: Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, edition: 5. Since the solution to 2.3.8 from 2.3 chapter was answered, more than 228 students have viewed the full step-by-step answer. Applied Partial Differential Equations with Fourier Series and Boundary Value Problems was written by and is associated to the ISBN: 9780321797056. The full step-by-step solution to problem: 2.3.8 from chapter: 2.3 was answered by , our top Math solution expert on 01/25/18, 04:21PM. This full solution covers the following key subjects: . This expansive textbook survival guide covers 81 chapters, and 759 solutions. The answer to “Consider u t = k 2u x2 u. This corresponds to a one-dimensional rod either with heat loss through the lateral sides with outside temperature 0 ( > 0, see Exercise 1.2.4) or with insulated lateral sides with a heat sink proportional to the temperature. Suppose that the boundary conditions are u(0, t) = 0 and u(L, t)=0. (a) What are the possible equilibrium temperature distributions if > 0? (b) Solve the time-dependent problem [u(x, 0) = f(x)] if > 0. Analyze the temperature for large time (t ) and compare to part (a).” is broken down into a number of easy to follow steps, and 94 words.

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