@Article{SanchezArinoKimmel1991,
  author     = {Sanchez, Eva and Arino, Ovide and Kimmel, Marek},
  title      = {Noncompact semigroups of operators generated by cell kinetics models},
  journal    = {Differential Integral Equations},
  year       = {1991},
  volume     = {4},
  number     = {6},
  pages      = {1233--1249},
  issn       = {0893-4983},
  abstract   = {We provide an analysis of the asymptotic behavior of
                  a noncompact semigroup of linear operators, based on
                  a general biological model describing unequal
                  division of cells. We demonstrate that the semigroup
                  exhibits, asymptotically, exponential growth; i.e.,
                  in the terms of the model, that the distribution
                  m(t,x) of cell size (x) in the dividing cells at a
                  given time (t) is equivalent to $\exp
                  (\lambda\sp*t)\mu\sp*(x)$, as t tends to
                  infinity. The semigroup operator is decomposed into
                  compact and noncompact parts and a bound on the
                  growth of the noncompact part is found. This step
                  includes an original technique of embedding the
                  problem into a family of related problems, which is
                  of potentially wider applicability. The method
                  employed in the paper hinges on the elementary
                  notion of continuous spectrum and provides an
                  alternative to analyses based on the more involved
                  notion of essential spectrum.},
  classmath  = {*47D06 One-parameter semigroups and linear evolution equations 92D25 Population dynamics 47N60 Appl. of operator theory in biology and other sciences 47A10 Spectrum and resolvent of linear operators},
  fjournal   = {Differential and Integral Equations. An International Journal for Theory and Applications},
  keywords   = {asymptotic behavior of a noncompact semigroup of linear operators; biological model describing unequal division of cells; exponential growth; continuous spectrum; essential spectrum},
  mrclass    = {47H20 (34K25 47N60 92C05)},
  mrnumber   = {93e:47090},
  mrreviewer = {V. N. Razzhevaikin},
}

{"_id":"GFDqFPTjisFta5Ek6","bibbaseid":"sanchez-arino-kimmel-noncompactsemigroupsofoperatorsgeneratedbycellkineticsmodels-1991","authorIDs":[],"author_short":["Sanchez, E.","Arino, O.","Kimmel, M."],"bibdata":{"bibtype":"article","type":"article","author":[{"propositions":[],"lastnames":["Sanchez"],"firstnames":["Eva"],"suffixes":[]},{"propositions":[],"lastnames":["Arino"],"firstnames":["Ovide"],"suffixes":[]},{"propositions":[],"lastnames":["Kimmel"],"firstnames":["Marek"],"suffixes":[]}],"title":"Noncompact semigroups of operators generated by cell kinetics models","journal":"Differential Integral Equations","year":"1991","volume":"4","number":"6","pages":"1233–1249","issn":"0893-4983","abstract":"We provide an analysis of the asymptotic behavior of a noncompact semigroup of linear operators, based on a general biological model describing unequal division of cells. We demonstrate that the semigroup exhibits, asymptotically, exponential growth; i.e., in the terms of the model, that the distribution m(t,x) of cell size (x) in the dividing cells at a given time (t) is equivalent to $\\exp (\\lambda\\sp*t)\\mu\\sp*(x)$, as t tends to infinity. The semigroup operator is decomposed into compact and noncompact parts and a bound on the growth of the noncompact part is found. This step includes an original technique of embedding the problem into a family of related problems, which is of potentially wider applicability. The method employed in the paper hinges on the elementary notion of continuous spectrum and provides an alternative to analyses based on the more involved notion of essential spectrum.","classmath":"*47D06 One-parameter semigroups and linear evolution equations 92D25 Population dynamics 47N60 Appl. of operator theory in biology and other sciences 47A10 Spectrum and resolvent of linear operators","fjournal":"Differential and Integral Equations. An International Journal for Theory and Applications","keywords":"asymptotic behavior of a noncompact semigroup of linear operators; biological model describing unequal division of cells; exponential growth; continuous spectrum; essential spectrum","mrclass":"47H20 (34K25 47N60 92C05)","mrnumber":"93e:47090","mrreviewer":"V. N. Razzhevaikin","bibtex":"@Article{SanchezArinoKimmel1991,\r\n author = {Sanchez, Eva and Arino, Ovide and Kimmel, Marek},\r\n title = {Noncompact semigroups of operators generated by cell kinetics models},\r\n journal = {Differential Integral Equations},\r\n year = {1991},\r\n volume = {4},\r\n number = {6},\r\n pages = {1233--1249},\r\n issn = {0893-4983},\r\n abstract = {We provide an analysis of the asymptotic behavior of\r\n a noncompact semigroup of linear operators, based on\r\n a general biological model describing unequal\r\n division of cells. We demonstrate that the semigroup\r\n exhibits, asymptotically, exponential growth; i.e.,\r\n in the terms of the model, that the distribution\r\n m(t,x) of cell size (x) in the dividing cells at a\r\n given time (t) is equivalent to $\\exp\r\n (\\lambda\\sp*t)\\mu\\sp*(x)$, as t tends to\r\n infinity. The semigroup operator is decomposed into\r\n compact and noncompact parts and a bound on the\r\n growth of the noncompact part is found. This step\r\n includes an original technique of embedding the\r\n problem into a family of related problems, which is\r\n of potentially wider applicability. The method\r\n employed in the paper hinges on the elementary\r\n notion of continuous spectrum and provides an\r\n alternative to analyses based on the more involved\r\n notion of essential spectrum.},\r\n classmath = {*47D06 One-parameter semigroups and linear evolution equations 92D25 Population dynamics 47N60 Appl. of operator theory in biology and other sciences 47A10 Spectrum and resolvent of linear operators},\r\n fjournal = {Differential and Integral Equations. An International Journal for Theory and Applications},\r\n keywords = {asymptotic behavior of a noncompact semigroup of linear operators; biological model describing unequal division of cells; exponential growth; continuous spectrum; essential spectrum},\r\n mrclass = {47H20 (34K25 47N60 92C05)},\r\n mrnumber = {93e:47090},\r\n mrreviewer = {V. N. Razzhevaikin},\r\n}\r\n\r\n","author_short":["Sanchez, E.","Arino, O.","Kimmel, M."],"key":"SanchezArinoKimmel1991","id":"SanchezArinoKimmel1991","bibbaseid":"sanchez-arino-kimmel-noncompactsemigroupsofoperatorsgeneratedbycellkineticsmodels-1991","role":"author","urls":{},"keyword":["asymptotic behavior of a noncompact semigroup of linear operators; biological model describing unequal division of cells; exponential growth; continuous spectrum; essential spectrum"],"downloads":0},"bibtype":"article","biburl":"https://server.math.umanitoba.ca/~jarino/ovide/papers/BiblioOvide.bib","creationDate":"2019-12-20T14:16:41.239Z","downloads":0,"keywords":["asymptotic behavior of a noncompact semigroup of linear operators; biological model describing unequal division of cells; exponential growth; continuous spectrum; essential spectrum"],"search_terms":["noncompact","semigroups","operators","generated","cell","kinetics","models","sanchez","arino","kimmel"],"title":"Noncompact semigroups of operators generated by cell kinetics models","year":1991,"dataSources":["DJzjnMX7p3giiS766"]}