Global existence of solutions to a chemotaxis system with volume filling effect

Tomasz Cieślak

Colloquium Mathematicae (2008)

  • Volume: 111, Issue: 1, page 117-134
  • ISSN: 0010-1354

Abstract

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A system of quasilinear parabolic equations modelling chemotaxis and taking into account the volume filling effect is studied under no-flux boundary conditions. The resulting system is non-uniformly parabolic. A Lyapunov functional for the system is constructed. The proof of existence and uniqueness of regular global-in-time solutions is given in cases when either the Lyapunov functional is bounded from below or chemotactic forces are suitably weakened. In the first case solutions are uniformly bounded in time, in the second one it is shown that a uniform bound is not possible.

How to cite

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Tomasz Cieślak. "Global existence of solutions to a chemotaxis system with volume filling effect." Colloquium Mathematicae 111.1 (2008): 117-134. <http://eudml.org/doc/283447>.

@article{TomaszCieślak2008,
abstract = {A system of quasilinear parabolic equations modelling chemotaxis and taking into account the volume filling effect is studied under no-flux boundary conditions. The resulting system is non-uniformly parabolic. A Lyapunov functional for the system is constructed. The proof of existence and uniqueness of regular global-in-time solutions is given in cases when either the Lyapunov functional is bounded from below or chemotactic forces are suitably weakened. In the first case solutions are uniformly bounded in time, in the second one it is shown that a uniform bound is not possible.},
author = {Tomasz Cieślak},
journal = {Colloquium Mathematicae},
keywords = {chemotaxis; global-in-time existence and uniqueness; quasilinear reaction-diffusion systems},
language = {eng},
number = {1},
pages = {117-134},
title = {Global existence of solutions to a chemotaxis system with volume filling effect},
url = {http://eudml.org/doc/283447},
volume = {111},
year = {2008},
}

TY - JOUR
AU - Tomasz Cieślak
TI - Global existence of solutions to a chemotaxis system with volume filling effect
JO - Colloquium Mathematicae
PY - 2008
VL - 111
IS - 1
SP - 117
EP - 134
AB - A system of quasilinear parabolic equations modelling chemotaxis and taking into account the volume filling effect is studied under no-flux boundary conditions. The resulting system is non-uniformly parabolic. A Lyapunov functional for the system is constructed. The proof of existence and uniqueness of regular global-in-time solutions is given in cases when either the Lyapunov functional is bounded from below or chemotactic forces are suitably weakened. In the first case solutions are uniformly bounded in time, in the second one it is shown that a uniform bound is not possible.
LA - eng
KW - chemotaxis; global-in-time existence and uniqueness; quasilinear reaction-diffusion systems
UR - http://eudml.org/doc/283447
ER -

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