=0 in (0,0) and T(x,t)= 0 at x= 0, l for all te[0,0).
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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![5. Consider a dynamics of heat conduction G in a bounded domain [0, €]:
= 0 in (0,€) and T(x,t)=0 at x= 0, l for all te[0, ∞).
ôt ôx
With the Lyapunov functional
V() =[r*(x,1)dx,
prove that G is asymptotically stable. (You may apply the LaSalle's principle.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc3a38ab4-8179-4deb-822f-ce9235deb09e%2F3c60e287-5032-47e0-b5b7-3f2b5ec99eac%2F5994vbd_processed.png&w=3840&q=75)
Transcribed Image Text:5. Consider a dynamics of heat conduction G in a bounded domain [0, €]:
= 0 in (0,€) and T(x,t)=0 at x= 0, l for all te[0, ∞).
ôt ôx
With the Lyapunov functional
V() =[r*(x,1)dx,
prove that G is asymptotically stable. (You may apply the LaSalle's principle.)
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