Global existence analysis of energy-reaction-diffusion systems

Abstract

We establish global-in-time existence results for thermodynamically consistent reaction-(cross-)diffusion systems coupled to an equation describing heat transfer. Our main interest is to model species-dependent diffusivities, while at the same time ensuring thermodynamic consistency. A key difficulty of the non-isothermal case lies in the intrinsic presence of cross-diffusion type phenomena like the Soret and the Dufour effect: due to the temperature/energy dependence of the thermodynamic equilibria, a nonvanishing temperature gradient may drive a concentration flux even in a situation with constant concentrations; likewise, a nonvanishing concentration gradient may drive a heat flux even in a case of spatially constant temperature. We use time discretisation and regularisation techniques and derive a priori estimates based on a suitable entropy and the associated entropy production. Renormalised solutions are used in cases where non-integrable diffusion fluxes or reaction terms appear.

To appear in SIAM Journal on Mathematical Analysis

References in corpus (1)

• The boundedness-by-entropy principle for cross-diffusion systems

Cited by in corpus (4)

• Weak-strong uniqueness for energy-reaction-diffusion systems
• Maximal mixed parabolic-hyperbolic regularity for the full equations of multicomponent fluid dynamics
• A brief overview of existence results and decay time estimates for a mathematical modeling of scintillating crystals
• Nonisothermal Richards flow in porous media with cross diffusion