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Article

Goursat Problem for the Factorizable Hyperbolic Equation in Two Independent Variables

by
I K. Johnpillai
* and
F M. Mahomed
*
School of Computational and Applied Mathematics, Centre for Differential Equations, Continuum Mechanics and Applications, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa
*
Authors to whom correspondence should be addressed.
Math. Comput. Appl. 2003, 8(1), 55-62; https://doi.org/10.3390/mca8010055
Published: 1 April 2003
Versions Notes

Abstract

For the scalar linear hyperbolic partial differential equations (PDEs) in two independent variables to be factorizable, the Laplace invariants h or k must be zero. In this paper, we find the Riemann function for the Goursat problem using the Lie group theoretical method where the hyperbolic . equation involved is factorized. What emerges is that the ordinary differential equation (ODE) whose solution gives the Riemann function for the Goursat problem is factorizable. Finally, an example is given as application of the methods
Keywords: Hyperbolic equation; Laplace invariants; Goursat problem Hyperbolic equation; Laplace invariants; Goursat problem

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MDPI and ACS Style

Johnpillai, I.K.; Mahomed, F.M. Goursat Problem for the Factorizable Hyperbolic Equation in Two Independent Variables. Math. Comput. Appl. 2003, 8, 55-62. https://doi.org/10.3390/mca8010055

AMA Style

Johnpillai IK, Mahomed FM. Goursat Problem for the Factorizable Hyperbolic Equation in Two Independent Variables. Mathematical and Computational Applications. 2003; 8(1):55-62. https://doi.org/10.3390/mca8010055

Chicago/Turabian Style

Johnpillai, I K., and F M. Mahomed. 2003. "Goursat Problem for the Factorizable Hyperbolic Equation in Two Independent Variables" Mathematical and Computational Applications 8, no. 1: 55-62. https://doi.org/10.3390/mca8010055

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