u(x,y,t_0) = \sin(\pi x)\,\sin(\pi y), & \qquad (x,y) \in \Omega.
\end{align}
An illustrative example of the numerical solution to the heat problem, using \eqref{ch5:eq:heatinit} as the initial condition is given in Figure \ref{ch5:fig:heatsolution}.
u(x,y,t_0) = \sin(\pi x)\,\sin(\pi y), & \qquad (x,y) \in \Omega.
\end{align}
An illustrative example of the numerical solution to the heat problem, using \eqref{ch5:eq:heatinit} as the initial condition is given in Figure \ref{ch5:fig:heatsolution}.