Global existence of renormalized solutions to entropy-dissipating reaction–diffusion systems Journal Article


Author(s): Fischer, Julian
Article Title: Global existence of renormalized solutions to entropy-dissipating reaction–diffusion systems
Affiliation
Abstract: In the present work we introduce the notion of a renormalized solution for reaction–diffusion systems with entropy-dissipating reactions. We establish the global existence of renormalized solutions. In the case of integrable reaction terms our notion of a renormalized solution reduces to the usual notion of a weak solution. Our existence result in particular covers all reaction–diffusion systems involving a single reversible reaction with mass-action kinetics and (possibly species-dependent) Fick-law diffusion; more generally, it covers the case of systems of reversible reactions with mass-action kinetics which satisfy the detailed balance condition. For such equations the existence of any kind of solution in general was an open problem, thereby motivating the study of renormalized solutions.
Journal Title: Archive for Rational Mechanics and Analysis
Volume: 218
Issue 1
ISSN: 1432-0673
Publisher: Springer  
Date Published: 2015-10-01
Start Page: 553
End Page: 587
Sponsor: This research was supported by the Lithuanian-Swiss cooperation program under the project agreement No. CH-SMM-01/0.
DOI: 10.1007/s00205-015-0866-x
Open access: no