Short time existence for coupling of scaled mean curvature flow and diffusion

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