Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 13 (2018), 159 -- 169

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Nezam Iraniparast

Abstract The study of small perturbations in the shock initiation of an inviscid compressible fluid with chemical reaction leads to a first order hyperbolic system of two equations. The order zero approximation of the system involves only constant coefficients. Here, we study a variation of this hyperbolic system and generalize it so that not all coefficients are constants. The boundary conditions in the first quadrant (t, x >0), where x is the spatial variable and t is time, include data along x = 0 and a proportionality relation between the dependent variables along t = 0. Using the characteristics of the system, we obtain explicit solutions.

2010 Mathematics Subject Classification: 35L40; 35L50
Keywords: hyperbolic system; characteristics; initial condition; boundary condition; asymptotic response

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Iraniparast Nezam
Western Kentucky University,
Bowling Green, Kentucky, USA.