# Interpretation of a PDE

1. Jan 14, 2012

### PhDorBust

Given $$\triangle u = f(x,y,z)$$ 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 $$u_t = k \triangle u$$, 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?

2. Jan 15, 2012

### PhDorBust

bump.. is something unclear?