Time-periodic solutions of advection-diffusion equations on moving   hypersurfaces
  In this paper we study time-periodic solutions to advection-diffusion equations of a scalar quantity $u$ on a periodically moving $n$-dimensional hypersurface $\Gamma(t) \subset \mathbb{R}^{n+1}$. We prove existence and uniqueness of solutions in suitable H\"older spaces. 
Charles M. Elliott and Hans Fritz
math.AP