Symmetries and conservation laws for a subclass of lubrication equations by using free software

摘要

Fourth-order nonlinear diffusion equations appear frequently in the description of physical processes, among these, the lubrication equation or the corresponding modified version play an important role in the study of the interface movements. In this work, we use the free software MAXIMA program symmgrp2009.max derived by W. Heremann to calculate the determining equations for the classical symmetries of the modified lubrication equation. We determine the subclasses of this equations which are self-adjoint and quasi-self adjoint. By using a general theorem on conservation laws proved by Nail Ibragimov we find conservation laws for some of these partial differential equations without classical Lagrangians.