Sonic and kinetic phase transitions with applications to Chapman-Jouguet deflagrations

We consider an n x n system of hyperbolic conservation laws and focus on the case of strongly under-determined sonic phase boundaries. We propose a Riemann solver that singles out solutions uniquely. This Riemann solver has two features: it selects phase boundaries by means of an exterior function and it allows compound waves. Then we prove the global existence of weak solutions to the Cauchy problem. Applications to Chapman-Jouguet deflagrations are given. Copyright (C) 2004 John Wiley Sons, Ltd.