Pattern formation instabilities on a curved shell

Pattern formation instabilities can be seen in various free surface flows. Dynamical pattern formation, that is, the initial nucleation and the consequent coarsening behaviour, is a rich source of problems that relate Marangoni effects, localised and global curvature and any external effects together. Here we look at a static case of the Turing-esq pattern formations on a curved shell as a result of the diffusion-reaction system.