Surveys in Mathematics and its Applications

ISSN1842-6298 (electronic), 1843-7265 (print)

Volume 13 (2018), 159 -- 169

This work is licensed under a Creative Commons Attribution 4.0 International License.## SOLUTIONS TO A FIRST ORDER HYPERBOLIC SYSTEM

## Nezam Iraniparast

AbstractThe 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

## References

David Logan,

Forced Response ot a Linear Hyperbolic System, Appl. Anal.33(1989), 255-266. MR1030112. Zbl 0653.35054.Wildon Fickett

Shock initiation of detonation in a dilute explosive, Phys. Fluids,27(1984), 94-105. Zbl 0543.76149.

Iraniparast Nezam

Western Kentucky University,

Bowling Green, Kentucky, USA.

e-mail: nezam.iraniparast@wku.edu