Symmetries of conservation laws

Abstract

We apply techniques of symmetry group analysis in solving two systems of conservation laws: a model of two strictly hyperbolic conservation laws and a zero pressure gas dynamics model, which both have no global so- lution, but whose solution consists of singular shock waves. We show that these shock waves are solutions in the sense of 1-strong association. Also, we compute all projectable symmetry groups and show that they are 1-strongly associated, hence transform existing solutions in the sense of 1-strong associ- ation into other solutions.