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.
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Fusco, D., Manganaro, N. A reduction approach for determining generalized simple waves. Z. angew. Math. Phys. 59, 63–75 (2008). https://doi.org/10.1007/s00033-006-5128-1
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DOI: https://doi.org/10.1007/s00033-006-5128-1