Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
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

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.2: Partial Derivatives
Problem 31E
See similar textbooks
icon
Related questions
Question

[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.)
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS