Abstract:

Over the last decade, phenomenon like electrowetting has led to advancements in lab-on-chips. Special fluids like ferrofluids have further technologically revolutionized numerous fields, including biomedical, for instance: magnetically guided drug delivery. In order to take the most advantage of these advances control of the underlying process is required. The PDEs involved are nonlinear, multiscale with typically unknown domains (free boundary problems) with a Young-Laplace equation on the free boundary to account for surface tension. We will discuss the analysis and approximation of the control of a model free boundary problem with surface tension. We end with a novel approach to realize the regularity of a Stokes problem with Navier slip boundary conditions which naturally appears in Stokes free boundary problem.