考虑一个带锥曲面上的四阶线性抛物方程,利用能量分析和逼近的方法,证明了方程在一个具有逼近性质的空间上的解的存在唯一性.最后,证明了当β∈(-1,0)时,对于一类函数这个性质等价于能量有限.“,”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).