A reduction approach for determining generalized simple waves

Abstract

A reduction approach is developed in order to construct generalized simple wave solutions to quasilinear nonhomogenous hyperbolic systems of first order PDEs. The solutions sought must possess a special ansatz which permits time-evolution of the profile of a simple wave due to a source-like term. These solutions involve a free function which can be used to fit classes of initial or boundary value problems. By means of the proposed approach two governing models of interest in a variety of applications are investigated. Model constitutive laws consistent with the full reduction process are obtained and the occurence of singularities at a finite time for the resulting solutions is analysed. Furthermore a comparison is made between the results obtained within the present theoretical framework and the standard simple wave solutions of the corresponding homogeneous (source free) governing models.