2013/10/17 by Martin Herberg, Martin Meyries, Herberg, Martin +6
Computer Science · Mathematics · Medicine · Physics and Astronomy · #35R35 #76D45 #76T10 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Dynamics and Pattern Formation #Opinion Dynamics and Social Influence #Secondary: 35Q30 #math.AP #math.DS #msc:35Q30 #msc:35R35 #msc:76D45 #msc:76T10
paper · pdf · doi:10.48550/arxiv.1310.4723
19 pages. Minor revision
openalex publication_date 2013/10/17 · arxiv created 2014/01/08 · arxiv updated 2014/01/09 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
The mass-based Maxwell-Stefan approach to one-phase multicomponent reactive mixtures is mathematically analyzed. It is shown that the resulting quasilinear, strongly coupled reaction-diffusion system is locally well-posed in an Lp-setting and generates a local semiflow on its natural state space. Solutions regularize instantly and become strictly positive if their initial components are all nonnegative and nontrivial. For a class of reversible mass-action kinetics, the positive equilibria are identified: these are precisely the constant chemical equilibria of the system, which may form a manifold. Here the total free energy of the system is employed which serves as a Lyapunov function for the system. By the generalized principle of linearized stability, positive equilibria are proved to be normally stable.