On weak solutions to a dissipative Baer-Nunziato-Type system for a mixture of two compressible heat conducting gases

In this paper, we consider a compressible dissipative Baer-Nunziato-Type system for a mixture of two compressible heat conducting gases. We prove that the set of weak solutions is stable, meaning that any sequence of weak solutions contains a (weakly) convergent subsequence whose limit is again a weak solution to the original system. Such type of results is usually considered as the most essential step to the proof of the existence of weak solutions. This is the first result of this type in the mathematical literature. Nevertheless, the construction of weak solutions to this system however remains still an (difficult) open problem.