Asymptotic behaviour of a non-autonomous population equation with diffusion in $L^1$ | Zendy

Abdelaziz Rhandi | Zendy; Roland Schnaubelt | Zendy

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Asymptotic behaviour of a non-autonomous population equation with diffusion in $L^1$

Author(s) -

Abdelaziz Rhandi,

Roland Schnaubelt

Publication year - 1999

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.1999.5.663

Subject(s) - extrapolation , mathematics , spectral radius , diffusion , population model , population , diffusion equation , position (finance) , radius , mathematical analysis , operator (biology) , asymptotic analysis , demography , physics , computer science , eigenvalues and eigenvectors , economics , economy , computer security , repressor , service (business) , chemistry , sociology , biochemistry , quantum mechanics , transcription factor , thermodynamics , finance , gene

We prove existence and uniquences of positive solutions of an age-structured population equation of McKendrick type with spatial diffusion in $L^1$. The coefficients may depend on age and position. Moreover, the mortality rate is allowed to be unbounded and the fertility rate is time dependent. In the time periodic case, we estimate the essential spectral radius of the monodromy operator which gives information on the asymptotic behaviour of solutions. Our work extends previous results in [19], [24], [30], and [31] to the non-autonomous situation. We use the theory of evolution semigroups and extrapolation spaces.

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