Focus on wellposedness results and dealing with moving boundaries and patterns
Biomedicine
– Two-phase flow for tissues and biofilms: Existence, uniqueness, and stability of solutions in the quasi-stationary approximation involving Compressible Stokes systems for the mixture’s mechanical behavior, Stationary transport equations for volume fractions, Convection-reaction-diffusion equations for chemical nutrients and signals.
na24
– Two-phase solid/fluid mixtures for tissues and biofilms: Compressible Stokes is replaced by elasticity. The quasistationary system is stabilized by deriving a pde for the velocity and closed with additional parabolic problems set in moving domains, for which a well posedness theory is developed.
amm23 mmas25
– Free boundaries: Thin film approximations to analyze how the boundaries of these multiphase mixtures evolve, which admit self-similar solutions.
entropy20
– Nonlocal transport model with moving boundary for cell death in response to antibiotics Wellposedness, finite time extinction results and control by means of bang-bang strategies and Bucy Kalman filters.
cnsns26
Materials
Mixed type systems for crystals: Perturbation methods to construct dislocation patterns in regions of mixed type.
siap01
