On the existence of Chapman-Jouguet detonation waves (Q2730748)

The authors study equations governing the detonation waves in a viscous combustible fluid. These equations of state are considered in a form that does not require any special assumptions on the reaction rate function. Travelling waves to such equations are investigated. The equations are reduced to a 4th-order system of ordinary differential equations with discontinuous right-hand sides. Some theorems on ordinary differential equations are proved. They imply the existence of heteroclinic solutions to these equations, which serve as the travelling waves for Chapman-Jouguet detonation.