Multicomponent Reactive Flows (ii) Asymptotic Stability of Equilibrium States

We consider the equations governing multicomponent reactive ows derived from the kinetic theory of dilute polyatomic reactive gas mixtures. We rst 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 ows using a normal form obtained in the previous part of the paper and the properties of Maxwellian chemical source terms.