| Autor: |
Huo, Xiaokai, Jüngel, Ansgar, Tzavaras, Athanasios E. |
| Rok vydání: |
2021 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
The weak-strong uniqueness for Maxwell--Stefan systems and some generalized systems is proved. The corresponding parabolic cross-diffusion equations are considered in a bounded domain with no-flux boundary conditions. The key points of the proofs are various inequalities for the relative entropy associated to the systems and the analysis of the spectrum of a quadratic form capturing the frictional dissipation. The latter task is complicated by the singular nature of the diffusion matrix. This difficulty is addressed by proving its positive definiteness on a subspace and using the Bott--Duffin matrix inverse. The generalized Maxwell--Stefan systems are shown to cover several known cross-diffusion systems for the description of tumor growth and physical vapor deposition processes. |
| Databáze: |
arXiv |
| Externí odkaz: |
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