Riemann Invariants and Rank-k Solutions of Hyperbolic Systems

Grundland, A. Michel and Huard, Benoit (2006) Riemann Invariants and Rank-k Solutions of Hyperbolic Systems. Journal of Nonlinear Mathematical Physics, 13 (3). pp. 393-419. ISSN 1402-9251

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Official URL: http://dx.doi.org/10.2991/jnmp.2006.13.3.6

Abstract

In this paper we employ a "direct method" in order to obtain rank-k solutions of any hyperbolic system of first order quasilinear differential equations in many dimensions. We discuss in detail the necessary and sufficient conditions for existence of these type of solutions written in terms of Riemann invariants. The most important characteristic of this approach is the introduction of specific first order side conditions consistent with the original system of PDEs, leading to a generalization of the Riemann invariant method of solving multi-dimensional systems of PDEs. We have demonstrated the usefulness of our approach through several examples of hydrodynamic type systems; new classes of solutions have been obtained in a closed form.

Item Type: Article
Subjects: G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Related URLs:
Depositing User: Benoit Huard
Date Deposited: 26 Mar 2013 14:06
Last Modified: 09 May 2017 05:27
URI: http://nrl.northumbria.ac.uk/id/eprint/11573

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