Multiple integral-balance method: Basic idea and an example with Mullin’s model of thermal grooving

A multiple integration technique of the integral-balance method allowing solving high-order diffusion equations is conceived in this note. The new method termed multiple-integral balance method is based on multiple integration procedures with respect to the space co-ordinate and is generalization of the widely applied heat-balance integral method of Goodman and the double integration method of Volkov. The method is demonstrated by a solution of the linear diffusion models of Mullins for thermal grooving