Group classification of a one-dimensional nonlinear poroelasticity equation

This paper studies a class of second order partial differential equations utt = f(ux)uxx + g(ut) arising in poroelasticity theory with arbitrary functions f(ux) and g(ut), using the group classification. It is shown that the principal Lie algebra of infinitely infinitesimal symmetries is three-dimensional. We use the method of a preliminary group classification for obtaining the classifications of these equations for a one-dimensional extension of the main Lie algebra.