A reduction approach for determining generalized simple waves |
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Authors: | Domenico Fusco Natale Manganaro |
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Institution: | (1) Department of Mathematics, University of Messina, Salita Sperone 31, 98166 Messina, Italy |
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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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Keywords: | 35L40 35N10 35D99 |
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