Group classification of one-dimensional equations of capillary fluids where the specific energy is a function of density, density gradient and entropy.

Abstract: An application of group analysis provides a regular procedure for mathematical modeling by classifying differential equations with respect to arbitrary elements. This paper presents the group classification of one-dimensional equations of fluids where the internal energy is a function of the density, the gradient of the density and the entropy. The group classification separates all models into 83 different classes according to the admitted Lie group. Some invariant solutions are studied. [Copyright &y& Elsevier]