Lie group analysis and invariant solutions of a pseudo-parabolic partial differential equation modelling solvent uptake in polymeric solids

Abstract

The main purpose of this work is to perform Lie group analysis of a pseudo-parabolic partial di erential equation modelling solvent uptake in polymeric solids. Three di erent sub-models for constitutive laws for the di usion coe cient and the viscosity will be considered. Once the symmetries have been determined, they will be used to nd groupinvariant solutions for the optimal systems of one-dimensional subalgebras obtained and where possible, exact solutions will be obtained.