I am presenting about optimal control of fluid flows through deformable porous media at the AWM Research Symposium.

There are many important biological and physical problems involving fluid flow through deformable, porous media. These problems are known as fluid-solid mixtures and have been studied considerably through well-posedness analysis and numerical investigations. The applications of these studies involve optimizing the biomechanical and fluid-dynamical responses of the fluid-solid mixture. Mathematically, this translates to optimization or optimal control problems subject to a partial differential equations (PDEs) system and the associated sensitivity analysis of the solution with respect to relevant physical or biological parameters.

I am working on studying relevant control and optimization related problems for fluid flows through porous media with applications to biomechanics. Results of this work could aid research in preventing microstructural tissue damage and designing bioengineered tissues. Most questions related to the sensitivity analysis and control of porous media flows are open in the field. I am focused on (1) well-posedness of optimal solutions and (2) necessary optimality conditions, which characterize the optimal control. These results are crucial for subsequent sensitivity calculations, parameter estimation, and derivative-based optimization algorithms.

This work is being done under the direction of Dr. Lorena Bociu within the Nonlinear Analysis Thematic Group at NC State.

Publications and Preprints