Abstract: A parabolic equation of fourth order on surfaces with conical singularities is considered. By the analysis of energy and approximations, the existence and uniqueness of the solution of this equation in a special space that has some approximation property are proved. Finally, it's proved that the property is equivalent to the finiteness of energy for some functions when β∈(-1,0).

Key words: parabolic equation, Calabi flow, conical singularity