We present a method for constructing similarity solutions of a fourth-order nonlinear partial differential equation for axisymmetric surface diffusion by extending an inverse method previously used for the second-order one-dimensional nonlinear diffusion equation. After imposing a solution profile, both a feasible surface tension, and a compatible mobility function are deduced simultaneously. Although the profile is not one-to-one, an optimization algorithm is implemented to construct a mobility function that is a function of surface orientation, with no practical difference in mobility between different arms of the many-to-one profile. It is shown that the solution of the linear model well approximates the solution of the nonlinear model, in which the surface tension and mobility are close to constant for a wide range of surface angles, even when nonlinear geometric terms are included.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics