Eventually positive semigroups of linear operators

By Daniel Daners, Jochen Gluck, James B. Kennedy. 2015

55 citations recorded by the source corpus.

Abstract We develop a systematic theory of eventually positive semigroups of linear operators mainly on spaces of continuous functions. By eventually positive we mean that for every positive initial condition the solution to the corresponding Cauchy problem is positive for large enough time. Characterisations of such semigroups are given by means of resolvent properties of the generator and Perron–Frobenius type spectral conditions. We apply these characterisations to prove eventual positivity of several examples of semigroups including some generated by fourth order elliptic operators and a delay differential equation. We also consider eventually positive semigroups on arbitrary Banach lattices and establish several results for their spectral bound which were previously only known for positive semigroups.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/b6faab9318330ba5feb43dc1852624d4b938c12f

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In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Eventually and asymptotically positive semigroups on Banach lattices (2015, methodology): “A first attempt to develop a unified theory of eventually positive C0-semigroups was subsequently made by the current authors in [18], providing some spectral results on Banach lattices and a characterisation of eventually strongly positive semigroups on C(K)-spaces with K compact.”