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Use the energy conservation solution with = 0 and theorem in Section A.1.) of the wave equation to prove that the only = 0 is u = 0. (Hint: Use the first vanishing

Use the energy conservation solution with = 0 and theorem in Section A.1.) of the wave equation to prove that the only = 0 is u = 0. (Hint: Use the first vanishing

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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[Second Order Equations] How do you solve question one thanks

1. Use the energy conservation of the wave equation to prove that the only solution with = 0 and ½ = 0 is u = 0. (Hint: Use the first vanishing theorem in Section A.1.)
Transcribed Image Text:1. Use the energy conservation of the wave equation to prove that the only solution with = 0 and ½ = 0 is u = 0. (Hint: Use the first vanishing theorem in Section A.1.)
First Vanishing Theorem. Let f(x) be a continuous function in D where D is a bounded domain. Assume that f(x) ≥ 0 in D and that ſſſ D f (x) dx = 0. Then f(x) is identically zero. (The proof of this theorem is similar to the one-dimensional case and is left to the reader.)
Transcribed Image Text:First Vanishing Theorem. Let f(x) be a continuous function in D where D is a bounded domain. Assume that f(x) ≥ 0 in D and that ſſſ D f (x) dx = 0. Then f(x) is identically zero. (The proof of this theorem is similar to the one-dimensional case and is left to the reader.)
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