ABSTRACT
In each of the above, the unknown u and the source term f are functions of the space and time variables. If f ≡ 0, we have, of course, the homogeneous versions of these equations.
Poisson’s equation: ∇2u = −f
Here, u and f are functions of the space variables. If f ≡ 0, we have
Laplace’s equation: ∇2u = 0
When separating out the time variable in the heat and wave equations, we encountered the
Convection or advection or linear transport equation: ut + v · ∇u = 0 Here, the velocity v is a function of the independent variables.
