journal article
LitStream Collection
Group classification of one-dimensional equations of fluids with internal energy depending on the density and the gradient of the density
doi: 10.1007/s00161-008-0088-7pmid: N/A
Group analysis provides a regular procedure for mathematical modeling by classifying differential equations with respect to arbitrary elements. This article presents the group classification of one-dimensional equations of fluids, where the internal energy is a function of the density and the gradient of the density. The equivalence Lie group and the admitted Lie group are provided. The group classification separates all models into 21 different classes according to the admitted Lie group. Invariant solutions of one particular model are obtained.