Weak-strong uniqueness for a class of degenerate parabolic cross-diffusion systems

Philippe Laurençot; Bogdan-Vasile Matioc

Archivum Mathematicum (2023)

  • Volume: 059, Issue: 2, page 201-213
  • ISSN: 0044-8753

Abstract

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Bounded weak solutions to a particular class of degenerate parabolic cross-diffusion systems are shown to coincide with the unique strong solution determined by the same initial condition on the maximal existence interval of the latter. The proof relies on an estimate established for a relative entropy associated to the system.

How to cite

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Laurençot, Philippe, and Matioc, Bogdan-Vasile. "Weak-strong uniqueness for a class of degenerate parabolic cross-diffusion systems." Archivum Mathematicum 059.2 (2023): 201-213. <http://eudml.org/doc/298971>.

@article{Laurençot2023,
abstract = {Bounded weak solutions to a particular class of degenerate parabolic cross-diffusion systems are shown to coincide with the unique strong solution determined by the same initial condition on the maximal existence interval of the latter. The proof relies on an estimate established for a relative entropy associated to the system.},
author = {Laurençot, Philippe, Matioc, Bogdan-Vasile},
journal = {Archivum Mathematicum},
keywords = {cross diffusion; weak-strong uniqueness; relative entropy},
language = {eng},
number = {2},
pages = {201-213},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Weak-strong uniqueness for a class of degenerate parabolic cross-diffusion systems},
url = {http://eudml.org/doc/298971},
volume = {059},
year = {2023},
}

TY - JOUR
AU - Laurençot, Philippe
AU - Matioc, Bogdan-Vasile
TI - Weak-strong uniqueness for a class of degenerate parabolic cross-diffusion systems
JO - Archivum Mathematicum
PY - 2023
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 059
IS - 2
SP - 201
EP - 213
AB - Bounded weak solutions to a particular class of degenerate parabolic cross-diffusion systems are shown to coincide with the unique strong solution determined by the same initial condition on the maximal existence interval of the latter. The proof relies on an estimate established for a relative entropy associated to the system.
LA - eng
KW - cross diffusion; weak-strong uniqueness; relative entropy
UR - http://eudml.org/doc/298971
ER -

References

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