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# Consider the Greens function G(x, t; x0, t0) for the wave equation. From (11.2.24) we ISBN: 9780321797056 284

## Solution for problem 11.2.9 Chapter 11.2

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

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Problem 11.2.9

Consider the Greens function G(x, t; x0, t0) for the wave equation. From (11.2.24) we easily obtain the influence functions for Q(x0, t0), u(x0, 0), and u/t0(x0, 0). These results may be obtained in the following alternative way: (a) For t>t0+ show that 2G t2 = c 22G, (11.2.43) where (by integrating from t0 to t0+) G(x, t0+; x0, t0) = 0 (11.2.44) G t (x, t0+; x0, t0) = (x x0). (11.2.45) From (11.2.32), briefly explain why G(x, t; x0, 0) is the influence function for u t0 (x0, 0). (b) Let = G/t. Show that for t>t0+, 2 t2 = c 22 (11.2.46) (x, t0+; x0, t0) = (x x0) (11.2.47) t (x, t0+; x0, t0)=0. (11.2.48) From (11.2.46)(11.2.48), briefly explain why G t0 (x, t; x0, 0) is the influence function for u(x0, 0).

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##### ISBN: 9780321797056

Since the solution to 11.2.9 from 11.2 chapter was answered, more than 221 students have viewed the full step-by-step answer. This full solution covers the following key subjects: . This expansive textbook survival guide covers 81 chapters, and 759 solutions. This textbook survival guide was created for the textbook: Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, edition: 5. The answer to “Consider the Greens function G(x, t; x0, t0) for the wave equation. From (11.2.24) we easily obtain the influence functions for Q(x0, t0), u(x0, 0), and u/t0(x0, 0). These results may be obtained in the following alternative way: (a) For t>t0+ show that 2G t2 = c 22G, (11.2.43) where (by integrating from t0 to t0+) G(x, t0+; x0, t0) = 0 (11.2.44) G t (x, t0+; x0, t0) = (x x0). (11.2.45) From (11.2.32), briefly explain why G(x, t; x0, 0) is the influence function for u t0 (x0, 0). (b) Let = G/t. Show that for t>t0+, 2 t2 = c 22 (11.2.46) (x, t0+; x0, t0) = (x x0) (11.2.47) t (x, t0+; x0, t0)=0. (11.2.48) From (11.2.46)(11.2.48), briefly explain why G t0 (x, t; x0, 0) is the influence function for u(x0, 0).” is broken down into a number of easy to follow steps, and 137 words. 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: 11.2.9 from chapter: 11.2 was answered by , our top Math solution expert on 01/25/18, 04:21PM.

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