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Suppose that u € C² (R²) and u(x, y) = 0 everywhere on the boundary of the square ((x,y): 0≤x≤ R,0 ≤ y ≤ R} QR a) Explain why it's true that if Uxx + Uyy = 0 everywhere in QR then u 0 in QR b) Show by example, that if uxx-Uyy = 0 everywhere in QR then u need not vanish in QR

Suppose that u € C² (R²) and u(x, y) = 0 everywhere on the boundary of the square ((x,y): 0≤x≤ R,0 ≤ y ≤ R} QR a) Explain why it's true that if Uxx + Uyy = 0 everywhere in QR then u 0 in QR b) Show by example, that if uxx-Uyy = 0 everywhere in QR then u need not vanish in QR

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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16. Suppose that u € C²(R²) and u(x, y) = 0 everywhere on the boundary of the square QR = {(x, y): 0 ≤ x ≤ R,0 ≤ y ≤ R} a) Explain why it's true that if uxx + Uyy = 0 everywhere in QR then u = 0 in QR b) Show by example, that if uxx - Uyy = 0 everywhere in QR then u need not vanish in QR
Transcribed Image Text:16. Suppose that u € C²(R²) and u(x, y) = 0 everywhere on the boundary of the square QR = {(x, y): 0 ≤ x ≤ R,0 ≤ y ≤ R} a) Explain why it's true that if uxx + Uyy = 0 everywhere in QR then u = 0 in QR b) Show by example, that if uxx - Uyy = 0 everywhere in QR then u need not vanish in QR
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