---
res:
bibo_abstract:
- 'We establish a weak–strong uniqueness principle for solutions to entropy-dissipating
reaction–diffusion equations: As long as a strong solution to the reaction–diffusion
equation exists, any weak solution and even any renormalized solution must coincide
with this strong solution. Our assumptions on the reaction rates are just the
entropy condition and local Lipschitz continuity; in particular, we do not impose
any growth restrictions on the reaction rates. Therefore, our result applies to
any single reversible reaction with mass-action kinetics as well as to systems
of reversible reactions with mass-action kinetics satisfying the detailed balance
condition. Renormalized solutions are known to exist globally in time for reaction–diffusion
equations with entropy-dissipating reaction rates; in contrast, the global-in-time
existence of weak solutions is in general still an open problem–even for smooth
data–, thereby motivating the study of renormalized solutions. The key ingredient
of our result is a careful adjustment of the usual relative entropy functional,
whose evolution cannot be controlled properly for weak solutions or renormalized
solutions.@eng'
bibo_authorlist:
- foaf_Person:
foaf_givenName: Julian L
foaf_name: Fischer, Julian L
foaf_surname: Fischer
foaf_workInfoHomepage: http://www.librecat.org/personId=2C12A0B0-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0002-0479-558X
bibo_doi: 10.1016/j.na.2017.03.001
bibo_volume: 159
dct_date: 2017^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/0362546X
dct_language: eng
dct_publisher: Elsevier@
dct_title: Weak–strong uniqueness of solutions to entropy dissipating reaction–diffusion
equations@
...