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2.* Consider the following heat system with U c R" open and bounded и, — Ди %3 f(x, 1) хEU, 1> 0 ди и + а— — () dv on ðU, и(х, 0) %3D 9(х), x € U where v is the outward unit normal to the boundary. Suppose that a(x) > 0 for any x e ôU (recall that u e C;(U × (0, 0)) U C(U × [0, 0)) to the above system. := Vu · v). Use the energy method to show that there is at most one solution dv

2.* Consider the following heat system with U c R" open and bounded и, — Ди %3 f(x, 1) хEU, 1> 0 ди и + а— — () dv on ðU, и(х, 0) %3D 9(х), x € U where v is the outward unit normal to the boundary. Suppose that a(x) > 0 for any x e ôU (recall that u e C;(U × (0, 0)) U C(U × [0, 0)) to the above system. := Vu · v). Use the energy method to show that there is at most one solution dv

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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2.* Consider the following heat system with U c R" open and bounded и, — Ди %3 f(x, 1) хEU, 1> 0 ди и + а— — () dv on ðU, и(х, 0) %3D 9(х), x € U where v is the outward unit normal to the boundary. Suppose that a(x) > 0 for any x e ôU (recall that u e C;(U × (0, 0)) U C(U × [0, 0)) to the above system. := Vu · v). Use the energy method to show that there is at most one solution dv
Transcribed Image Text:2.* Consider the following heat system with U c R" open and bounded и, — Ди %3 f(x, 1) хEU, 1> 0 ди и + а— — () dv on ðU, и(х, 0) %3D 9(х), x € U where v is the outward unit normal to the boundary. Suppose that a(x) > 0 for any x e ôU (recall that u e C;(U × (0, 0)) U C(U × [0, 0)) to the above system. := Vu · v). Use the energy method to show that there is at most one solution dv
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