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Well-posedness and Asymptotic Behaviour of Non-autonomous Linear Evolution Equations

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Evolution Equations, Semigroups and Functional Analysis

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 50))

Abstract

There is a striking difference between autonomous and non-autonomous linear evolution equations. Autonomous problems are well understood in the framework of strongly continuous operator semigroups and their generalizations. The Hille-Yosida type theorems settle the question of well-posedness to a great extend, many perturbation and approximation results have been established, and for a large class of problems the asymptotic behaviour can be studied on the basis of spectral theory and transform methods. In these and many other areas semigroup theory has reached a considerable degree of maturity, and its applications thrive in plenty of fields.

To the memory of Brunello Terreni

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  1. FB Mathematik und Informatik, Martin-Luther-Universität, Theodor-Lieser-Str. 5, D-06120, Halle, Germany

    Roland Schnaubelt

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  1. Roland Schnaubelt
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  1. Dipartimento di Matematica, Università degli Studi di Milano, 20133, Milano, Italy

    Alfredo Lorenzi  & Bernhard Ruf  & 

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Schnaubelt, R. (2002). Well-posedness and Asymptotic Behaviour of Non-autonomous Linear Evolution Equations. In: Lorenzi, A., Ruf, B. (eds) Evolution Equations, Semigroups and Functional Analysis. Progress in Nonlinear Differential Equations and Their Applications, vol 50. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8221-7_17

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  • DOI: https://doi.org/10.1007/978-3-0348-8221-7_17

  • Publisher Name: Birkhäuser, Basel

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