Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN: 9781133382119
Author: Swokowski
Publisher: Cengage
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![26.6 Problem. To prove uniqueness for (26.2), we would want to show that if u solves
U₁ = Uxx, 0 ≤ x ≤ L, t>0
u(x, 0) = 0, 0 ≤ x ≤ L
lim(st)(2.0+) u(s, t) = 0
(26.4)
u(0,t) = u(L,t) = 0, t≥0.
then u = 0. Reread the proof of the preceding theorem and explain why it still works for
(26.4). [Hint: the subtle point is that maybe E is now only differentiable on (0,∞). Why?
Does that really matter?]
U₁ = xx 0 ≤ x ≤L, t> 0
Uxx, t>0
ut
u(x, 0) = f(x), 0 ≤ x ≤ L
lim (s,t)→(2,0+) u(s, t) = f(x)
u(0,t) = a(t), u(L,t) = b(t), t≥ 0.
(26.2)](https://content.bartleby.com/qna-images/question/690bc708-737a-4036-8bde-cd8ee17ec8dd/477a013d-d147-47d4-a752-0dbdebd1bf09/u17hg2w_thumbnail.jpeg)
Transcribed Image Text:26.6 Problem. To prove uniqueness for (26.2), we would want to show that if u solves
U₁ = Uxx, 0 ≤ x ≤ L, t>0
u(x, 0) = 0, 0 ≤ x ≤ L
lim(st)(2.0+) u(s, t) = 0
(26.4)
u(0,t) = u(L,t) = 0, t≥0.
then u = 0. Reread the proof of the preceding theorem and explain why it still works for
(26.4). [Hint: the subtle point is that maybe E is now only differentiable on (0,∞). Why?
Does that really matter?]
U₁ = xx 0 ≤ x ≤L, t> 0
Uxx, t>0
ut
u(x, 0) = f(x), 0 ≤ x ≤ L
lim (s,t)→(2,0+) u(s, t) = f(x)
u(0,t) = a(t), u(L,t) = b(t), t≥ 0.
(26.2)
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