On the causality of real‐valued semigroups and diffusion |
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Authors: | Richard Kowar |
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Institution: | Department of Mathematics, University of Innbruck, , A‐6020, Innsbruck, Austria |
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Abstract: | In this paper, we show that a process modeled by a strongly continuous real‐valued semigroup (that has a space convolution operator as infinitesimal generator) cannot satisfy causality. We present and analyze a causal model of diffusion that satisfies the semigroup property at a discrete set of time points and that is in contrast to the classical diffusion model not smooth. More precisely, if v denotes the concentration of a substance diffusing with constant speed, then v is continuous, but its time derivative is discontinuous at the discrete set M of time points. Furthermore, we show that diffusion with constant speed satisfies an inhomogeneous wave equation with a time dependent coefficient. Copyright © 2011 John Wiley & Sons, Ltd. |
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Keywords: | diffusion semigroups causality |
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