Geodesic
Entropy of scalar reaction-diffusion equations
Mathematica Bohemica, Tome 139 (2014) no. 4, pp. 597-605

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MR Zbl
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.
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.
DOI : 10.21136/MB.2014.144137
Classification : 35B40, 37A35, 37B40, 37L30
Keywords: reaction-diffusion equation; attractor; invariant measure; entropy; Poincaré-Bendixson theorem 
Slijepčević, Siniša. Entropy of scalar reaction-diffusion equations. Mathematica Bohemica, Tome 139 (2014) no. 4, pp. 597-605. doi: 10.21136/MB.2014.144137
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