Display Abstract

Title Estimates in $W^{1,\infty}$ for generalized Forchheimer equations in porous media

Name Luan T Hoang
Country USA
Email luan.hoang@ttu.edu
Co-Author(s) Thinh Kieu and Tuoc Phan
Submit Time 2014-02-25 17:07:15
Special Session 60: Recent advances in evolutionary equations
We consider generalized Forchheimer (non-Darcy) flows of slightly compressible fluids in porous media. The resulting degenerate parabolic equation for pressure is studied in a bounded domain with time-dependent boundary data. We obtain long-time estimates for the $L^\infty$-norm of the pressure, its gradient and time derivative. Exploiting the special structure of the equation, we combine the De Giorgi and Ladyzhenskaya-Uraltseva iteration techniques with uniform Gronwall-type inequalities. This is joint work with Thinh Kieu and Tuoc Phan.