Level set method - defining the velocity

Hi all,

I want to solve this simple system using level set methods. The model has moving boundary.

The velocity of the boundary is given by,
V= -∇〖P|〗_∂Ω.n_∂Ω+ G∇〖Γ|〗_∂Ω.n_∂Ω- AG 〖(n.x)|〗_∂Ω/2
(please refer to the attached file)

For example for the give pde,
(∇^2.Γ) - Γ = 0

I don't know how to calculate the Γ value along the boundary (∂Ω(t)), where phi = 0.5 (conservative level set method in comsol)

attached is a small description of my model and the coupled equations.

Thank you very much
Ashan