Solutions to a first order hyperbolic system

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.

Keywords

• hyperbolic system
• characteristics
• initial condition
• boundary condition
• asymptotic response