Goursat Problem for the Factorizable Hyperbolic Equation in Two Independent Variables

I K. Johnpillai; F M. Mahomed

doi:10.3390/mca8010055

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1 April 2003

Goursat Problem for the Factorizable Hyperbolic Equation in Two Independent Variables

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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

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Math. Comput. Appl.2003, 8(1), 55-62;https://doi.org/10.3390/mca8010055

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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

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