Evolution semigroups for nonautonomous Cauchy problems.

Nickel, Gregor

Displaying similar documents to “Evolution semigroups for nonautonomous Cauchy problems.”

On two-parameter regularized semigroups and the Cauchy problem.

Janfada, Mohammad (2009)

Abstract and Applied Analysis

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Mild integrated C-existence families

Shen Wang (1995)

Studia Mathematica

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We study mild n times integrated C-existence families without the assumption of exponential boundedness. We present several equivalent conditions for these families. Hille-Yosida type necessary and sufficient conditions are given for the exponentially bounded case.

Regularized semigroups and systems of linear partial differential equations

M. Hieber, A. Holderrieth, F. Neubrander (1992)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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$B$ -bounded semigroups and implicit evolution equations.

Banasiak, J. (2000)

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On α-times integrated C-semigroups and the abstract Cauchy problem

Chung-Cheng Kuo, Sen-Yen Shaw (2000)

Studia Mathematica

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This paper is concerned with α-times integrated C-semigroups for α > 0 and the associated abstract Cauchy problem: $u^{'} (t) = A u (t) + \frac{t^{α - 1}}{Γ (α)} x$ , t >0; u(0) = 0. We first investigate basic properties of an α-times integrated C-semigroup which may not be exponentially bounded. We then characterize the generator A of an exponentially bounded α-times integrated C-semigroup, either in terms of its Laplace transforms or in terms of existence of a unique solution of the above abstract Cauchy problem for every x...