Work

A Lumer–Phillips type generation theorem for bi-continuous semigroups

Year: 2022

Type: article

Abstract: The famous 1960s Lumer–Phillips theorem states that a closed and densely defined operator A\colon \operatorname{D}(A)\subseteq X \to X on a Banach space X generates a strongly continuous contraction semigroup if and only if (A,\operatorname{D}(A)) is dissipative and the range of \lambda-A is surjective in X for some \lambda>0 . In this paper, we establish a version of this result for bi-continuous semigroups and apply the latter amongst other examples to the transport equation as well as to flows on infinite networks.

Source: Zeitschrift für Analysis und ihre Anwendungen

DOI: 10.4171/zaa/1695

Authors: Christian Budde, Sven-Ake Wegner

Institutions: University of the Free State, Universität Hamburg

Language: German

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Deutscher Akademischer Austauschdienst, Deutsche Forschungsgemeinschaft

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