Does the following function for temperature satisfy the heat equation when there is no heat generation ( \(\alpha\) is thermal diffusivity):

\[T=T_{0}+T_{m} \exp \left(\frac{-2 \pi^{2} \alpha}{L^{2}} t\right) \sin \left(\frac{\pi x}{L}\right) \sin \left(\frac{\pi y}{L}\right)\]

You may assume \(L, T_{0}\), and \(T_{m}\) are also constant.