Semigroup applications everywhere

Semigroup applications everywhere

Most dynamical systems arise from partial differential equations (PDEs) that can be represented as an abstract evolution equation on a suitable state space complemented by an initial or final condition. Thus, the system can be written as a Cauchy problem on an abstract function space with appropriat...

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Veröffentlicht in:Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences physical, and engineering sciences, 2020-11, Vol.378 (2185), p.1-6
Hauptverfasser: Nagel, Rainer, Rhandi, Abdelaziz
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Sprache:eng
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Introduction
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Rhandi, Abdelaziz
description Most dynamical systems arise from partial differential equations (PDEs) that can be represented as an abstract evolution equation on a suitable state space complemented by an initial or final condition. Thus, the system can be written as a Cauchy problem on an abstract function space with appropriate topological structures. To study the qualitative and quantitative properties of the solutions, the theory of one-parameter operator semigroups is a most powerful tool. This approach has been used by many authors and applied to quite different fields, e.g. ordinary and PDEs, nonlinear dynamical systems, control theory, functional differential and Volterra equations, mathematical physics, mathematical biology, stochastic processes. The present special issue of Philosophical Transactions includes papers on semigroups and their applications. This article is part of the theme issue ‘Semigroup applications everywhere’.
doi_str_mv 10.1098/rsta.2019.0610rsta20190610
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ispartof Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences, 2020-11, Vol.378 (2185), p.1-6
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subjects Introduction
title Semigroup applications everywhere
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