Fischer, Julian and Hopf, Katharina and Kniely, Michael and Mielke, Alexander
(2022)
*Global existence analysis of energy-reaction-diffusion systems. SIAM Journal on Mathematical Analysis.*
SIAM Journal on Mathematical Analysis, 54
.
pp. 220-267.

Full text not available from this repository.

Official URL: https://doi.org/10.1137/20M1387237

## 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.

Item Type: | Article |
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Subjects: | Mathematical and Computer Sciences Mathematical and Computer Sciences > Mathematics Mathematical and Computer Sciences > Mathematics > Applied Mathematics |

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics |

ID Code: | 3173 |

Deposited By: | Lukas-Maximilian Jaeger |

Deposited On: | 05 Sep 2024 08:39 |

Last Modified: | 05 Sep 2024 08:39 |

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