Abstract
The elementary wave interactions for the Chapman-Jouguet model with combustion are investigated. We obtain the unique solution of the initial value problem under the global entropy conditions. We analyze the elementary wave interactions in the phase plane and construct uniquely the solution of this initial value problem. It is found that the combustion wave solution of the corresponding Riemann may be extinguished after perturbation which shows that the unburnt gas is unstable.
Highlights
In this paper, we study the following equations ( ) (ρρt ( ρ + x =0, u ) t ρu2 + p x E ( ρuE pu = 0, (1) q x, t
In [4], the authors investigated the two-dimensional Riemann problem for isentropic Chaplygin gas dynamic system according to different combinations of four elementary waves and they delivered a complete classification to the above problem
For the wave interaction between the shock wave and the detonation wave, we find that it may extinguish the combustion wave which shows that the unburnt gas is unstable
Summary
If sup T ( x, y) > Ti ; 0≤ y≤t otherwise, where ρ,u, p < 0 , T are the density, velocity, pressure, temperature respectively. In [4], the authors investigated the two-dimensional Riemann problem for isentropic Chaplygin gas dynamic system according to different combinations of four elementary waves and they delivered a complete classification to the above problem. The authors [6] investigated several two-dimensional Riemann problems for Chaplygin gas model and proved the existence of the unique solution. In [7], the authors studied the appearance of delta shock wave and vacuum state in the vanishing pressure limit of Riemann solutions to the non-isentropic generalized Chaplygin gas equations. In [12] the authors studied the following selfsimilar ZND model ut + px = 0, τqEtt(−x+,u(txu) p= = )0−x ,= kt φ0,(T ) q.
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