Flow control of fluids through porous media

This paper discusses flow control of fluids through porous media, specifically related to its application in petroleum science. The flow of fluids is described by the Boussinesq equation with mixed boundary conditions; a Neumann boundary condition describes no flow at the outer boundary of the porous media and a nonlinear boundary condition describes the interaction between the porous media and the source potential. In many ways, the source potential can be controlled. This leads to a boundary control problem of the Boussinesq equation. The problem can be analyzed by the Lyapunov method. Numerical examples are performed to provide a clear understanding of the concept of boundary control for these fluid flow systems.