Communications in Mathematical Sciences

Volume 7 (2009)

Number 1

Fluid-dynamc model equations for a gas with slow reversible biomolecular reactions

Pages: 143 – 163



Maria Groppi

Alberto Rossani

Giampiero Spiga


The dispersion relation and shock structure of a gas mixture undergoing a bimolecular chemical reaction are studied by means of a hydrodynamic model deduced from the relevant kinetic equations. Qualitative changes in the solution, in particular loss of smoothness, for varying parameters (including Mach number and strength of the chemical reaction rate) are investigated, and numerical results are presented. In the limits of vanishing or diverging reactive relaxation times the "equilibrium" and "frozen" thermodynamical situations are recovered.


Reactive gas mixtures; shock wave structure; dispersion relation; hydrodynamic limits

2010 Mathematics Subject Classification

76A02, 76L05, 76V05, 82C40

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