Diff between poisson equation and laplace equation
Answers
Answer:
The only difference, as you say, is the right-hand side:
Δu=f
where the special case f=0 is the Laplace equation.
The physical intuition is that f is a "source term": if you think of the Poisson equation as describing the steady state temperature of a region, when f=0 you are assuming heat enters and leaves only through the boundary, whereas when f≠0 you are including some "hot plates" in the interior as well. The same intuition also applies when you interpret the Poisson equation as describing an electric potential: f now is the charge density on the interior. And the same also applies for the gravitational potential and mass density.
The special case gets its own name since the solutions of the Laplace equation are harmonic and have very special properties, such as the maximum principle etc.
✔️Hope it will help you.✔️