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Asymptotic behavior for a class of the renewal nonlinear equation with diffusion
Author(s) -
Michel Philippe,
Touaoula Tarik Mohamed
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2591
Subject(s) - uniqueness , mathematics , convergence (economics) , nonlinear system , class (philosophy) , diffusion , diffusion equation , term (time) , mathematical analysis , boundary (topology) , computer science , physics , economy , service (business) , quantum mechanics , artificial intelligence , economics , thermodynamics , economic growth
In this paper, we consider nonlinear age‐structured equation with diffusion under nonlocal boundary condition and non‐negative initial data. More precisely, we prove that under some assumptions on the nonlinear term in a model of McKendrick–Von Foerster with diffusion in age, solutions exist and converge (long‐time convergence) towards a stationary solution. In the first part, we use classical analysis tools to prove the existence, uniqueness, and the positivity of the solution. In the second part, using comparison principle, we prove the convergence of this solution towards the stationary solution. Copyright © 2012 John Wiley & Sons, Ltd.