About: Age-Structured Population Dynamics with Nonlocal Diffusion

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An Entity of Type : schema:ScholarlyArticle, within Data Space : wasabi.inria.fr associated with source document(s)

Attributes	Values
type	Academic Article research paper schema:ScholarlyArticle
isDefinedBy	Covid-on-the-Web dataset
has title	Age-Structured Population Dynamics with Nonlocal Diffusion
Creator	Yu, Xiao Ruan, Shigui Kang, Hao
Source	Medline; PMC
abstract	Random diffusive age-structured population models have been studied by many researchers. Though nonlocal diffusion processes are more applicable to many biological and physical problems compared with random diffusion processes, there are very few theoretical results on age-structured population models with nonlocal diffusion. In this paper our objective is to develop basic theory for age-structured population dynamics with nonlocal diffusion. In particular, we study the semigroup of linear operators associated to an age-structured model with nonlocal diffusion and use the spectral properties of its infinitesimal generator to determine the stability of the zero steady state. It is shown that (i) the structure of the semigroup for the age-structured model with nonlocal diffusion is essentially determined by that of the semigroups for the age-structured model without diffusion and the nonlocal operator when both birth and death rates are independent of spatial variables; (ii) the asymptotic behavior can be determined by the sign of spectral bound of the infinitesimal generator when both birth and death rates are dependent on spatial variables; (iii) the weak solution and comparison principle can be established when both birth and death rates are dependent on spatial variables and time; and (iv) the above results can be generalized to an age-size structured model. In addition, we compare our results with the age-structured model with Laplacian diffusion in the first two cases (i) and (ii).
has issue date	2020-06-15(xsd:dateTime)
bibo:doi	10.1007/s10884-020-09860-5
bibo:pmid	32837120
has license	no-cc
sha1sum (hex)	6b2ac7122b8c556ba86afa324d2b0e2a12e59e69
schema:url	https://doi.org/10.1007/s10884-020-09860-5
resource representing a document's title	Age-Structured Population Dynamics with Nonlocal Diffusion
has PubMed Central identifier	PMC7299252
has PubMed identifier	32837120
schema:publication	J Dyn Differ Equ
resource representing a document's body	covid:6b2ac7122b8c556ba86afa324d2b0e2a12e59e69#body_text
is schema:about of	named entity 'BEHAVIOR' named entity 'PHYSICAL' named entity 'AGE' named entity 'age-structured' named entity 'asymptotic behavior' named entity 'diffusion processes' named entity 'nonlocal operator' named entity 'diffusion' named entity 'steady state' named entity 'spectral properties' named entity 'death rates' named entity 'infinitesimal generator' named entity 'Population Dynamics' named entity 'Age-Structured' named entity 'semigroup' named entity 'essential spectrum' named entity 'age structure' named entity 'resolvent' named entity 'nonlinear' named entity 'spectral theorem' named entity 'initial data' named entity 'death rate' named entity 'semigroup' named entity 'infinitesimal generator' named entity 'nonautonomous' named entity 'Cauchy problem' named entity 'contraction mapping' named entity 'Banach lattice' named entity 'semigroup' named entity 'state space' named entity 'resolvent set' named entity 'spectral radius' named entity '1.1' named entity '1, 2' named entity 'essential norm' named entity 'semigroup' named entity 'one-dimensional' named entity 'resolvent' named entity 'Laplace' named entity '1, 2' named entity 'boundary conditions' named entity 'Pazy' named entity 'steady state' named entity '2.11' named entity 'Banach' named entity 'orthonormal basis' named entity 'Europe' named entity 'positive operator' named entity 'initial data' named entity 'strictly decreasing' named entity 'eigenfunctions' named entity 'Laplace' named entity '4.14' named entity 'bounded linear operator' named entity 'spectral properties' named entity '5.5' named entity 'eigenspace' named entity 'eigenvalue' named entity 'von Foerster' named entity 'semigroup' named entity 'infinitesimal generator' named entity 'asymptotic expression' named entity 'R N' named entity 'essential norm' named entity 'Metz' named entity 'nonlocal operator' named entity '3.8' named entity 'state space' named entity '5.1' named entity 'eigenvectors' named entity 'eigenvalue' named entity 'semigroup' named entity 'strongly continuous' named entity 'eigenvalue' named entity 'Laplace' named entity 'functional equations' named entity 'monotonic' named entity 'population dynamics' named entity 'lemmas and theorems'

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