1 Introduction

2 Baer-Nunziato-type models with barotropic equation of state  
2.1 Evolution equations  
2.2 Some remarks on thermodynamics  
2.3 Relaxation Model  

3 Mathematical Properties  
3.1 Hyperbolicity: eigenvectors and eigenvalues  
3.2 Characteristic fields  
3.3 Riemann invariants  
3.4 Symmetrization  

4 Mathematical Entropy  
4.1 Isothermal case  
4.2 Isentropic case  

5 Relaxation to equilibrium  
5.1 Isothermal case  
5.2 Isentropic case  

6 Numerical results  
6.1 Discretization  
6.2 Validation  

7 Conclusion