Mark
Consider the heat problem
$$
\begin{array}{ll}
u_t = ku_{xx} & u(x,0) = f(x) \\
u(0,t) = 0 & u(1,t) = t/(t+1),
\end{array}
$$
where the initial temperature distribution $f(x)$ looks like so:
Sketch the steady state solution along with the evolution towards that steady state.
