# Entropy of scalar reaction-diffusion equations

Mathematica Bohemica (2014)

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

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topSlijepčević, 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 -

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