---
_id: '10547'
abstract:
- lang: eng
text: "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,\r\nwhile 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."
acknowledgement: M.K. gratefully acknowledges the hospitality of WIAS Berlin, where
a major part of the project was carried out. The research stay of M.K. at WIAS Berlin
was funded by the Austrian Federal Ministry of Education, Science and Research through
a research fellowship for graduates of a promotio sub auspiciis. The research of
A.M. has been partially supported by Deutsche Forschungsgemeinschaft (DFG) through
the Collaborative Research Center SFB 1114 “Scaling Cascades in Complex Systems”
(Project no. 235221301), Subproject C05 “Effective models for materials and interfaces
with multiple scales”. J.F. and A.M. are grateful for the hospitality of the Erwin
Schrödinger Institute in Vienna, where some ideas for this work have been developed.
The authors are grateful to two anonymous referees for several helpful comments,
in particular for the short proof of estimate (2.7).
article_processing_charge: No
article_type: original
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Katharina
full_name: Hopf, Katharina
last_name: Hopf
- first_name: Michael
full_name: Kniely, Michael
id: 2CA2C08C-F248-11E8-B48F-1D18A9856A87
last_name: Kniely
orcid: 0000-0001-5645-4333
- first_name: Alexander
full_name: Mielke, Alexander
last_name: Mielke
citation:
ama: Fischer JL, Hopf K, Kniely M, Mielke A. Global existence analysis of energy-reaction-diffusion
systems. SIAM Journal on Mathematical Analysis. 2022;54(1):220-267. doi:10.1137/20M1387237
apa: Fischer, J. L., Hopf, K., Kniely, M., & Mielke, A. (2022). Global existence
analysis of energy-reaction-diffusion systems. SIAM Journal on Mathematical
Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/20M1387237
chicago: Fischer, Julian L, Katharina Hopf, Michael Kniely, and Alexander Mielke.
“Global Existence Analysis of Energy-Reaction-Diffusion Systems.” SIAM Journal
on Mathematical Analysis. Society for Industrial and Applied Mathematics,
2022. https://doi.org/10.1137/20M1387237.
ieee: J. L. Fischer, K. Hopf, M. Kniely, and A. Mielke, “Global existence analysis
of energy-reaction-diffusion systems,” SIAM Journal on Mathematical Analysis,
vol. 54, no. 1. Society for Industrial and Applied Mathematics, pp. 220–267, 2022.
ista: Fischer JL, Hopf K, Kniely M, Mielke A. 2022. Global existence analysis of
energy-reaction-diffusion systems. SIAM Journal on Mathematical Analysis. 54(1),
220–267.
mla: Fischer, Julian L., et al. “Global Existence Analysis of Energy-Reaction-Diffusion
Systems.” SIAM Journal on Mathematical Analysis, vol. 54, no. 1, Society
for Industrial and Applied Mathematics, 2022, pp. 220–67, doi:10.1137/20M1387237.
short: J.L. Fischer, K. Hopf, M. Kniely, A. Mielke, SIAM Journal on Mathematical
Analysis 54 (2022) 220–267.
date_created: 2021-12-16T12:08:56Z
date_published: 2022-01-04T00:00:00Z
date_updated: 2023-08-02T13:37:03Z
day: '04'
department:
- _id: JuFi
doi: 10.1137/20M1387237
external_id:
arxiv:
- '2012.03792 '
isi:
- '000762768000006'
intvolume: ' 54'
isi: 1
issue: '1'
keyword:
- Energy-Reaction-Diffusion Systems
- Cross Diffusion
- Global-In-Time Existence of Weak/Renormalised Solutions
- Entropy Method
- Onsager System
- Soret/Dufour Effect
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2012.03792
month: '01'
oa: 1
oa_version: Preprint
page: 220-267
publication: SIAM Journal on Mathematical Analysis
publication_identifier:
issn:
- 0036-1410
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Global existence analysis of energy-reaction-diffusion systems
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 54
year: '2022'
...