Given [tex] \triangle u = f(x,y,z)[/tex] on a given body with vanishing neumann boundary conditions. I'm asked to interpret it in terms of heat and diffusion. Since heat/diffusion take the form [tex] u_t = k \triangle u[/tex], I am a little confused as I there is no time term here. I think the answer is that u denotes the concentration of heat/substance and the PDE is saying that no heat/substance will escape the body. The process is time invariant, so the PDE is just defining the distribution of heat/substance inside the body to follow this strange rule that its laplacian is f? Is this reasoning correct? Can I assign some physical intuition to the distribution of heat/substance inside the body following the rule that its laplacian be f?