Huo, X., Jüngel, A., & Tzavaras, A. E. (2022). Weak-Strong Uniqueness for Maxwell-Stefan Systems. SIAM Journal on Mathematical Analysis, 54(3), 3215–3252. https://doi.org/10.1137/21M145210X
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 with 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.
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Project title:
Emergente Netzwerkstrukturen und neuromorphische Anwendungen: 101018153 (European Commission) Derivation and analysis of cross-diffusion systems: P 30000-N32 (Fonds zur Förderung der wissenschaftlichen Forschung (FWF)) Multikomponentensysteme mit unvollständiger Diffusion: P 33010-N (Fonds zur Förderung der wissenschaftlichen Forschung (FWF)) Langzeitverhalten von diskreten dissipativen Systemen: F6503-N36 (Fonds zur Förderung der wissenschaftlichen Forschung (FWF)) Doktoratskolleg "Dissipation and Dispersion in Nonlinear Partial Differential Equations": W1245-N25 (Fonds zur Förderung der wissenschaftlichen Forschung (FWF))
