  We consider a diffusion process on an evolving surface with a piecewise
Lipschitz-continuous boundary from an energetic point of view. We employ an
energetic variational approach with both surface divergence and transport
theorems to derive the generalized diffusion and heat systems on the evolving
surface. Moreover, we investigate the boundary conditions for the two systems
to study the conservation and energy laws of them. As an application, we make a
mathematical model for a diffusion process on an evolving double bubble.
Especially, this paper is devoted to deriving the representation formula for
the unit outer co-normal vector to the boundary of a surface.
