A Signalling Problem for Near-Equilibrium Flows in the Fickett-Majda Model of Combustion

The signalling problem for chemico-acoustic interactions ina simplified model of combustion and detonation is considered.The problem is examined in different limits, depending uponthe sensitivity of the reaction rate with the degree of reactioncoordinate and with the thermodynamic state. In one limit, theproblem is singular, and singular perturbation techniques areused to obtain an approximate solution. In the general case,a combination Riemann function-Laplace transform method is usedto obtain exact solutions with arbitrary boundary data. Thiscombined method allows the Riemann method to be applied to certainwave problems with discontinuous data.