Special Session 108: New Developments in porous media

Studying generalized Forchheimer flows in heterogeneous porous media

Emine Celik
Texas Tech University
Co-Author(s):    Luan Hoang
We study the generalized Forchheimer flows of slightly compressible fluids in heterogeneous porous media where the derived nonlinear partial differential equation for the pressure can be singular and degenerate in the spatial variables, in addition to being degenerate for large pressure gradient. Suitable weighted Lebesgue norms for the pressure, its gradient and time derivative are estimated. The continuous dependence on the initial and boundary data is established for the pressure and its gradient with respect to those corresponding norms. Asymptotic estimates are derived even for unbounded boundary data as time tends to infinity. We also obtain the estimates for the $L^\infty$-norms of the pressure and its time derivative by implementing De Giorgi`s iteration in the context of the above weighted norms. This is a joint work with Luan Hoang.