Positive perturbation of operator semigroups: Growth bounds, essential compactness, and asynchronous exponential growth

Research output: Contribution to journalArticle

27 Scopus citations

Abstract

If B is the generator of an increasing locally Lipschitz continuous integrated semigroup on an abstract L space X and C : D(B) → X perturbs B positively, then A = B+C is again the generator of an increasing I.L.c. integrated semigroup. In this paper we study the growth bound and the compactness properties of the C0 semigroup So that is generated by the part of A in Xo = D(B). We derive conditions in terms of the resolvent outputs F(λ) = C(λ - B)-1 for the semigroup So to be eventually compact or essentially compact and to exhibit asynchronous exponential growth. We apply our results to age-structured population models with additional structures. We consider an age-structured model with spatial diffusion and an age-size-structured model.

Original languageEnglish (US)
Pages (from-to)735-764
Number of pages30
JournalDiscrete and Continuous Dynamical Systems
Volume4
Issue number4
DOIs
StatePublished - Jan 1 1998

Keywords

  • Asynchronous exponential growth
  • Cumulative outputs
  • Eventual and essential compactness
  • Growth bounds
  • Integrated semigroups
  • Positive perturbation
  • Resolvent outputs
  • Resolvent positive operator
  • Semigroups
  • Spectral bound
  • Stieltjes integral equations

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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