OK, I agree the eq is nonlinear, but what if I need to consider that term of the gradient magnitude. Would it be more appropriate to move the LaPlacian & the zeroth order term of X to the other side of the eq & square it to get rid of the sq root? Then you have a Helmholtz eq that is squared & you pick a value for the gradient that is considered a nominal value for the gradient magnitude for a defined region.
Then the Helmholtz eq is = to the sq root of some constant.
Can pdesolve work then?
I am not on a machine right now with MAPLE so I have not tried.
+ do you know any literature that is pretty standard on approaching such a problem? I am in the process of chasing something down via internet today on XMAS.