申論題

Problem 1 (20%) ป็น 8น Let u be a solution to the heat equation: with boundary conditions: u(0, x) = f(x), O ≤ s  ≤ I, and=0, 0≤t＜∞. 

(a) (10%) Define the thermal energyu(t,x)da. Show that under the above assumptions, T(t)

is constant in time; i.e., f(x)dr, for all t≥0.