# Determining rotation of a bending detachment fault system

I would like to obtain the angle of rotation (𝛿θ) of a detachment fault (or oceanic core complex) after X meters of rock displaced during spreading at a mid-ocean ridge. I have a differential equation that can describe the elastic behavior of this fault:

$\nabla^2(D\nabla^2w) + \rho g w = p$

with D the flexural rigidity, w the deflection, ρ the material density, g the gravitational constant, and p the load. Source and details: https://ic.ucsc.edu/~casey/eart150/Death%20Valley%20Reading/Buck,1988_Rolling%20Hinge.pdf

I am not quite sure how to handle this. My aim is to plot 𝛿θ against X so that I get curve models showing an fast increased of fault rotation for a certain distance of spreading, and a steady-flat evolution afterwards (showing nearly no rotation happening anymore).

I never did any geodynamic modelling before but I'm able to work days/nights to get those curves.

If someone could give me a hint about the process (how to approach the problem mathematically or how to start), I would appreciate greatly.