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MATHEMATICA BOHEMICA, Vol. 139, No. 4, pp. 597-605, 2014
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Entropy of scalar reaction-diffusion equations

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Siniša Slijepčević

* Siniša Slijepčević*, Department of Mathematics, University of Zagreb, Bijenička 30, Croatia, e-mail: ` slijepce@math.hr`

**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.

**Keywords:** reaction-diffusion equation; attractor; invariant measure; entropy; Poincaré-Bendixson theorem

**Classification (MSC 2010):** 37L30, 37A35, 37B40, 35B40

**Full text** available as PDF.

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