Global existence analysis of energy-reaction-diffusion systems. SIAM Journal on Mathematical Analysis

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 nonisothermal 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 discretization and regularization techniques and derive a priori estimates based on a suitable entropy and the associated entropy production. Renormalized solutions are used in cases where nonintegrable diffusion fluxes or reaction terms appear.