The generalized riemann problem for a scalar nonconvex chapman-jouguet combustion model

The generalized Riemann problem for a scalar nonconvex Chapman-Jouget combustion model in a neighborhood of the origin ( t > 0) on the ( x, t) plane is considered. Under the entropy conditions, we exhibit the construction of the solutions. It can be observed that, for some cases, there are essential differences between the structures of the perturbed Riemann solutions and the corresponding Riemann solutions. Especially, a strong detonation in the corresponding Riemann solution may turn into a weak deflagration followed by a shock wave after perturbation, which appears in the numerical simulations of Bao and Jin [J. Comput. Phys., 163 (2000), pp. 216-248] and Zhang and Ying [J. Comput. Math., 23 (2005), pp. 337-350].