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Abstract
The signalling problem for chemico-acoustic interactions in a simplified model of combustion and detonation is considered. The problem is examined in different limits, depending upon the sensitivity of the reaction rate with the degree of reaction coordinate and with the thermodynamic state. In one limit, the problem is singular, and singular perturbation techniques are used to obtain an approximate solution. In the general case, a combination Riemann function-Laplace transform method is used to obtain exact solutions with arbitrary boundary data. This combined method allows the Riemann method to be applied to certain wave problems with discontinuous data.
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