Lie symmetry analysis of a pseudoparabolic PDE: Power law in diffusion coefficient with constant viscosity

Abstract

We perform symmetry analysis of a partial differential equation (PDE) of pseudoparabolic form which models solvent uptake in polymeric solids; a special case of power law for diffusion coefficient and constant viscosity is considered. Optimal systems of one-dimensional subalgebras for various model parameters are employed for symmetry reductions and construction of invariant solutions. • A phenomenon of case II diffusion in glassy polymers is considered. • A model equation is an implicit pseudoparabolic partial differential equation which incorporates the diffusion coefficient and viscosity of the polymer. • The model equation is studied from Lie symmetry analysis view point for a special case of power law in diffusion coefficient and constant viscosity. • Some exact solutions are obtained and presented graphically.