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...

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Extracted 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.)