---
_id: '712'
abstract:
- lang: eng
  text: '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.'
author:
- first_name: Julian L
  full_name: Fischer, Julian L
  id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
  last_name: Fischer
  orcid: 0000-0002-0479-558X
citation:
  ama: 'Fischer JL. Weak–strong uniqueness of solutions to entropy dissipating reaction–diffusion
    equations. <i>Nonlinear Analysis: Theory, Methods and Applications</i>. 2017;159:181-207.
    doi:<a href="https://doi.org/10.1016/j.na.2017.03.001">10.1016/j.na.2017.03.001</a>'
  apa: 'Fischer, J. L. (2017). Weak–strong uniqueness of solutions to entropy dissipating
    reaction–diffusion equations. <i>Nonlinear Analysis: Theory, Methods and Applications</i>.
    Elsevier. <a href="https://doi.org/10.1016/j.na.2017.03.001">https://doi.org/10.1016/j.na.2017.03.001</a>'
  chicago: 'Fischer, Julian L. “Weak–Strong Uniqueness of Solutions to Entropy Dissipating
    Reaction–Diffusion Equations.” <i>Nonlinear Analysis: Theory, Methods and Applications</i>.
    Elsevier, 2017. <a href="https://doi.org/10.1016/j.na.2017.03.001">https://doi.org/10.1016/j.na.2017.03.001</a>.'
  ieee: 'J. L. Fischer, “Weak–strong uniqueness of solutions to entropy dissipating
    reaction–diffusion equations,” <i>Nonlinear Analysis: Theory, Methods and Applications</i>,
    vol. 159. Elsevier, pp. 181–207, 2017.'
  ista: 'Fischer JL. 2017. Weak–strong uniqueness of solutions to entropy dissipating
    reaction–diffusion equations. Nonlinear Analysis: Theory, Methods and Applications.
    159, 181–207.'
  mla: 'Fischer, Julian L. “Weak–Strong Uniqueness of Solutions to Entropy Dissipating
    Reaction–Diffusion Equations.” <i>Nonlinear Analysis: Theory, Methods and Applications</i>,
    vol. 159, Elsevier, 2017, pp. 181–207, doi:<a href="https://doi.org/10.1016/j.na.2017.03.001">10.1016/j.na.2017.03.001</a>.'
  short: 'J.L. Fischer, Nonlinear Analysis: Theory, Methods and Applications 159 (2017)
    181–207.'
date_created: 2018-12-11T11:48:05Z
date_published: 2017-08-01T00:00:00Z
date_updated: 2021-01-12T08:11:55Z
day: '01'
department:
- _id: JuFi
doi: 10.1016/j.na.2017.03.001
intvolume: '       159'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1703.00730
month: '08'
oa: 1
oa_version: Submitted Version
page: 181 - 207
publication: 'Nonlinear Analysis: Theory, Methods and Applications'
publication_identifier:
  issn:
  - 0362546X
publication_status: published
publisher: Elsevier
publist_id: '6975'
quality_controlled: '1'
scopus_import: 1
status: public
title: Weak–strong uniqueness of solutions to entropy dissipating reaction–diffusion
  equations
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 159
year: '2017'
...