Hi

Consider Poisson equation with Neumann boundary condition but the right hand side of boundary condition is in term of the unknown function $u$. How we can solve it?

$\Delta u(x) = f(x)\quad in~ \Omega$

$\frac{\partial u(x)}{\partial n }=g(u(x))\quad on~\partial \Omega$

where n is outward normal vector.

For special case let $g=\sqrt u$.

very muchon the form of $g$ and so I think one needs to reduce it to cases. – Dorian Oct 9 '10 at 2:17