Double-wave solutions to quasilinear hyperbolic systems of first-order PDEs

Double-wave solutions to quasilinear hyperbolic systems of first-order PDEs A reduction procedure for determining double-wave exact solutions to first-order hyperbolic systems of PDEs is proposed. The basic idea is to reduce the integration of the governing hyperbolic set of N partial differential equations to that of a $$2 \times 2$$ 2 × 2 reduced hyperbolic model along with a further differential constraint. Therefore, the method of differential constraints is used in order to solve the auxiliary $$2 \times 2$$ 2 × 2 system. An example of interest to viscoelasticity is presented. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Zeitschrift für angewandte Mathematik und Physik Springer Journals

Double-wave solutions to quasilinear hyperbolic systems of first-order PDEs

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer International Publishing AG
Subject
Engineering; Theoretical and Applied Mechanics; Mathematical Methods in Physics
ISSN
0044-2275
eISSN
1420-9039
D.O.I.
10.1007/s00033-017-0850-4
Publisher site
See Article on Publisher Site

Abstract

A reduction procedure for determining double-wave exact solutions to first-order hyperbolic systems of PDEs is proposed. The basic idea is to reduce the integration of the governing hyperbolic set of N partial differential equations to that of a $$2 \times 2$$ 2 × 2 reduced hyperbolic model along with a further differential constraint. Therefore, the method of differential constraints is used in order to solve the auxiliary $$2 \times 2$$ 2 × 2 system. An example of interest to viscoelasticity is presented.

Journal

Zeitschrift für angewandte Mathematik und PhysikSpringer Journals

Published: Aug 19, 2017

References

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