ASYMPTOTIC STABILITY OF EQUILIBRIUM STATES FOR MULTICOMPONENT REACTIVE FLOWS

We consider the equations governing multicomponent reactive flows deri ved from the kinetic theory of dilute polyatomic reactive gas mixtures . Using an entropy function, we derive a symmetric conservative form o f the system. In the framework of Kawashima and Shizuta's theory, we r ecast the resulting system into a normal form, that is, in the form of a symmetric hyperbolic-parabolic composite system. We also characteri ze all normal forms for symmetric systems of conservation laws such th at the null space associated with dissipation matrices is invariant. W e then investigate an abstract second-order quasilinear system with a source term, around a constant equilibrium state. Assuming the existen ce of a generalized entropy function, the invariance of the null space naturally associated with dissipation matrices, stability conditions for the source term, and a dissipative structure for the linearized eq uations, 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 reac tive hows using a normal form and the properties of Maxwellian chemica l source terms.