MULTICOMPONENT REACTIVE FLOWS

(II) ASYMPTOTIC STABILITY OF EQUILIBRIUM STATES 


Vincent GIOVANGIGLI and Marc MASSOT

 
Centre de Math\'ematiques Appliqu\'ees

Ecole Polytechnique, 91128 Palaiseau Cedex, France




We consider the equations governing  multicomponent reactive flows 
derived from the kinetic theory of dilute polyatomic reactive gas 
mixtures. We first discuss the structure of the chemical source term 
associated with Maxwellian distributions. We then investigate an
abstract second order quasilinear system  with a source term,
around a constant equilibrium state.  Assuming  the existence 
a generalized entropy function, the invariance of the nullspace 
naturally associated with dissipation matrices, stability conditions
for the source term, and a dissipative structure for the linearized 
equations, we establish  global existence and asymptotic stability 
around the constant equilibrium state in all space dimensions and 
we obtain decay estimates. These results are then applied to 
multicomponent reactive flows using a normal form obtained in the 
previous part of the paper and the properties of Maxwellian 
chemical source terms.


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