By the Kirchhoff integral transformation , a class of nonlinear parabolic equations can be converted to a class of linear one , A boundary integral equation for the linear one and a boundary variational formulation are presented. In addition to the indication of existence and uniqueness of the solution of this equation using lax-milgram theorem , the Kirchhoff integral transformation in the nonlinear coefficient based on a set of discrete data is given by a piece wise linear polynomial.