Structural stability of generalized Forchheimer equations for compressible fluids in porous media

We study the generalized Forchheimer equations for slightly compressible fluids in porous media. The structural stability is established with respect to either the boundary data or the coefficients of the Forchheimer polynomials. A weighted Poincaré-Sobolev inequality related to the nonlinearity of the equation is used to study the asymptotic behaviour of the solutions. Moreover, we prove a perturbed monotonicity property of the vector field associated with the resulting non-Darcy equation, where the correction is explicit and Lipschitz continuous in the coefficients of the Forchheimer polynomials.