MATHEMATICA BOHEMICA, Vol. 139, No. 4, pp. 597-605, 2014

Entropy of scalar reaction-diffusion equations

Siniša Slijepčević

Siniša Slijepčević, Department of Mathematics, University of Zagreb, Bijenička 30, Croatia, e-mail:

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

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