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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