Entropy of scalar reaction-diffusion equations

Siniša Slijepčević

Mathematica Bohemica (2014)

  • Volume: 139, Issue: 4, page 597-605
  • ISSN: 0862-7959

Abstract

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We consider scalar reaction-diffusion equations on bounded and extended domains, both with the autonomous and time-periodic nonlinear term. We discuss the meaning and implications of the ergodic Poincaré-Bendixson theorem to dynamics. In particular, we show that in the extended autonomous case, the space-time topological entropy is zero. Furthermore, we characterize in the extended nonautonomous case the space-time topological and metric entropies as entropies of a pair of commuting planar homeomorphisms.

How to cite

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Slijepčević, Siniša. "Entropy of scalar reaction-diffusion equations." Mathematica Bohemica 139.4 (2014): 597-605. <http://eudml.org/doc/269839>.

@article{Slijepčević2014,
abstract = {We consider scalar reaction-diffusion equations on bounded and extended domains, both with the autonomous and time-periodic nonlinear term. We discuss the meaning and implications of the ergodic Poincaré-Bendixson theorem to dynamics. In particular, we show that in the extended autonomous case, the space-time topological entropy is zero. Furthermore, we characterize in the extended nonautonomous case the space-time topological and metric entropies as entropies of a pair of commuting planar homeomorphisms.},
author = {Slijepčević, Siniša},
journal = {Mathematica Bohemica},
keywords = {reaction-diffusion equation; attractor; invariant measure; entropy; Poincaré-Bendixson theorem; reaction-diffusion equation; attractor; invariant measure; entropy; Poincaré-Bendixson theorem},
language = {eng},
number = {4},
pages = {597-605},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Entropy of scalar reaction-diffusion equations},
url = {http://eudml.org/doc/269839},
volume = {139},
year = {2014},
}

TY - JOUR
AU - Slijepčević, Siniša
TI - Entropy of scalar reaction-diffusion equations
JO - Mathematica Bohemica
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 139
IS - 4
SP - 597
EP - 605
AB - We consider scalar reaction-diffusion equations on bounded and extended domains, both with the autonomous and time-periodic nonlinear term. We discuss the meaning and implications of the ergodic Poincaré-Bendixson theorem to dynamics. In particular, we show that in the extended autonomous case, the space-time topological entropy is zero. Furthermore, we characterize in the extended nonautonomous case the space-time topological and metric entropies as entropies of a pair of commuting planar homeomorphisms.
LA - eng
KW - reaction-diffusion equation; attractor; invariant measure; entropy; Poincaré-Bendixson theorem; reaction-diffusion equation; attractor; invariant measure; entropy; Poincaré-Bendixson theorem
UR - http://eudml.org/doc/269839
ER -

References

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