Consider the following partial differential equation:
$\frac{\partial y(x,t)}{\partial t} = \theta \nabla^2y(x,t)$
where $x \in R^2$ is the spatial index and $t \in Z^+$ is the temporal index. Can you please confirm if the Laplacian operation is obtained from the Hessian matrix which is $3 \times 3$ (spatial and temporal factors) or $2 \times 2$ (only spatial factors) ?
I do not know much about PDEs and my apologizes if this question is too elementary.