@Article{Arino1992,
  author     = {Arino, Ovide},
  title      = {Some spectral properties for the asymptotic behavior of semigroups connected to population dynamics},
  journal    = {SIAM Rev.},
  year       = {1992},
  volume     = {34},
  number     = {3},
  pages      = {445--476},
  issn       = {0036-1445},
  abstract   = {In this paper one may find valuable information
                  related to the study of asymptotic behavior of
                  semigroups which arise from some structured models
                  of population dynamics (such as the Sharpe-Lotka
                  age-dependent model and models of cell
                  proliferation). The author reviews classical notions
                  and results of the spectral theory of operators (a
                  special emphasis is done on perturbing the essential
                  spectrum) and also he treats the relation between
                  the spectrum of the generator and the asymptotic
                  behavior of the semigroup (specially in the case of
                  positive semigroups). The theoretical results are
                  applied to a model of cell populations.},
  classmath  = {*92D25 Population dynamics 47D03 (Semi)groups of linear operators 47B60 Operators on ordered spaces 47A10 Spectrum and resolvent of linear operators 47B65 Positive and order bounded operators  },
  coden      = {SIREAD},
  fjournal   = {SIAM Review. A Publication of the Society for Industrial and Applied Mathematics},
  keywords   = {asynchronous exponential growth; spectral perturbations; asymptotic behavior of semigroups; structured models of population dynamics; Sharpe-Lotka age-dependent model; models of cell proliferation; positive semigroups},
  mrclass    = {47D06 (34G10 47B65 47N20 92D25)},
  mrnumber   = {93h:47051},
  mrreviewer = {R. Nagel},
  pdf        = {Arino-1992-SIREV34.pdf},
  reviewer   = {A.Canada (Granada)},
}

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