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Let u be a solution of the heat equation U, –u = 0 u(0,1)= u(7,t)=0 ; u(x,0)= sin x+sin 2x ; 00 %3D ; t>0 Then. 1: (a) u(x,t)→0 as t→o for all xe (0,7) (b) t'u(x,t)→0 as t→ 0 for all x e (0,7) (c) e'u(x,t) is a bounded function for xe (0, 7),t >0 (d) e'u(x,t)→0 'as t→o for all xe(0,7) 6.

Let u be a solution of the heat equation U, –u = 0 u(0,1)= u(7,t)=0 ; u(x,0)= sin x+sin 2x ; 00 %3D ; t>0 Then. 1: (a) u(x,t)→0 as t→o for all xe (0,7) (b) t'u(x,t)→0 as t→ 0 for all x e (0,7) (c) e'u(x,t) is a bounded function for xe (0, 7),t >0 (d) e'u(x,t)→0 'as t→o for all xe(0,7) 6.

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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Let u be a solution of the heat equation u, -Uxx ; 0<x<T and t>0 u(0,t)=u(r,t)=0 u(x,0)= sin x+ sin 2x; 0<x<n ; t>0 Then. 1: (a) u(x,t)→0 as t→o for all x e (0,7) (b) t'u(x,t)→0 as t→o for all xe (0, (c) - e'u(x,t) is a bounded function for xe (0,7),t >0 (d) e"u(x,t)→0 as t→o for all xe (0,7)
Transcribed Image Text:Let u be a solution of the heat equation u, -Uxx ; 0<x<T and t>0 u(0,t)=u(r,t)=0 u(x,0)= sin x+ sin 2x; 0<x<n ; t>0 Then. 1: (a) u(x,t)→0 as t→o for all x e (0,7) (b) t'u(x,t)→0 as t→o for all xe (0, (c) - e'u(x,t) is a bounded function for xe (0,7),t >0 (d) e"u(x,t)→0 as t→o for all xe (0,7)
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