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On the Riemann Problem for a Scalar Zeldovich-von Neumann-Döring Combustion Model

We consider the Riemann problem for Majda's Zeldovich--von Neumann--Doring (ZND) combustion model with a “bump-type" ignition function proposed by Lyng and Zumbrun [Phys. D, 194 (2004), pp. 1--29]. The global existence of piecewise smooth entropy solutions is obtained constructively. These solutions involve detonation and deflagration waves. The limiting behavior of deflagration wave solutions to the Riemann problem when the reacting rate tends to infinity is also considered.