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On weak solutions to a dissipative Baer-Nunziato-type system for a mixture of two compressible heat conducting gases. (English) Zbl 1450.35218

Summary: 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.

MSC:

35Q35 PDEs in connection with fluid mechanics
35Q49 Transport equations
76N06 Compressible Navier-Stokes equations
76N15 Gas dynamics (general theory)
80A19 Diffusive and convective heat and mass transfer, heat flow
35B35 Stability in context of PDEs
35D30 Weak solutions to PDEs
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