Approximation of a degenerate semilinear PDE with a nonlinear Neumann boundary condition

We consider a system of semilinear partial differential equations (PDEs) with nonlinearity depending on both the solution and its gradient. The Neumann boundary condition depends in nonlinear manner. uniform ellipticity is not required for diffusion coefficient. show that this problem admits viscosity which can be approximated by penalization. Lipschitz coefficients part. part as well are Lipschitz. Moreover, monotone variable. Note existence to has been established [13] then completed [15]. In present paper, we construct sequence penalized systems decoupled forward backward stochastic (FBSDEs) directly strong convergence. This allows us deal case where Our work extends, particular, result [4] and, some sense, those [1, 3]. contrast works 3, 4], do pass weak compactness laws associated our problem.