Time-Periodic Solutions of Advection-Diffusion Equations on Moving Hypersurfaces
Charles M. Elliott, Hans Fritz · SIAM Journal on Mathematical Analysis · 2015
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 Hölder spaces.