The large diffusion limit for the heat equation with a dynamical boundary condition

We study the heat equation on a half-space with a linear dynamical boundary condition. Our main aim is to show that, if the diffusion coefficient tends to infinity, then the solutions converge (in a suitable sense) to solutions of the Laplace equation with the same dynamical boundary condition.

The 2D dynamics of the differentially rotating envelope of massive stars

We build a 2D model of the radiative envelope of main sequence massive stars. We set a dynamical boundary condition at the bottom of the radiative envelope at η = rC/R (where rC is the core size and R the radius of the star) to account for the differential rotation of the convective core as computed in 3D simulations (e.g. Browning et al. (2004, IAUS, 224, 149). We seek the differential rotation and associated meridional circulation induced by such a shear competing with the baroclinic flow of the stably stratified radiative envelope using the Boussinesq approximation.