Use the solution of PDE tool box as known function to solve another PDE

I solved the simple Laplace equation on a certain geometry, and now want to use a certain combination (nonlinear) of the solution function as source term of a new Poisson equation. How do I do this?

The problem arises because of two reasons:

My system is:

\theta_xx + \theta_yy = 0 (certain boundary conditions)

\omega_xx + \omega_yy = (\theta_xx - \theta_yy)*sin(\theta) (certain boundary conditions)

\psi_xx + \psi_yy = \omega

so three decoupled equations, but I would need the symbolic expressions to use repeatedly the pde toolbox.

[Dario Cortese]

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