Weak-Strong Uniqueness for Maxwell--Stefan Systems

The weak-strong uniqueness for Maxwell--Stefan systems and some generalized is proved. corresponding parabolic cross-diffusion equations are considered in a bounded domain with no-flux boundary conditions. key points of the proofs various inequalities relative entropy associated analysis spectrum quadratic form capturing frictional dissipation. latter task complicated by singular nature diffusion matrix. This difficulty addressed proving its positive definiteness on subspace using Bott--Duffin matrix inverse. shown to cover several known description tumor growth physical vapor deposition processes.