  We prove a short time existence result for a system consisting of a geometric
evolution equation for a hypersurface and a parabolic equation on this evolving
hypersurface. More precisely, we discuss a mean curvature flow scaled with a
term that depends on a quantity defined on the surface coupled to a diffusion
equation for that quantity. The proof is based on a splitting ansatz, solving
both equations separately using linearization and a contraction argument. Our
result is formulated for the case of immersed hypersurfaces and yields a
uniform lower bound on the existence time that allows for small changes in the
initial value of the height function.
