@article{10547,
  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.},
  author       = {Fischer, Julian L and Hopf, Katharina and Kniely, Michael and Mielke, Alexander},
  issn         = {0036-1410},
  journal      = {SIAM Journal on Mathematical Analysis},
  keywords     = {Energy-Reaction-Diffusion Systems, Cross Diffusion, Global-In-Time Existence of Weak/Renormalised Solutions, Entropy Method, Onsager System, Soret/Dufour Effect},
  number       = {1},
  pages        = {220--267},
  publisher    = {Society for Industrial and Applied Mathematics},
  title        = {{Global existence analysis of energy-reaction-diffusion systems}},
  doi          = {10.1137/20M1387237},
  volume       = {54},
  year         = {2022},
}