(3) Let $u(x, t)$ satisfy the heat flow model $$ \left\{\begin{array}{1} u_{t}=k u_{xx} W u(0, t)=u(L, t=0 W u(x, 0)=u_{0} (x) \end{array} ight. $$ for $x \in(O, $ and $t>0$. Show that $$ \int_{0}^{L) u(x, t)^{2} d x \leq Vint_{0}^{L) u_{0} (X)^{2} d x $$ for $t \geq 0$. CS.SD.067