General relative entropy in a nonlinear McKendrick model
Résumé
We use the General Relative Entropy Inequality introduced in [12, 13, 14] to analyze the long time convergence in a nonlinear renewal equation, a PDE that describes age structured populations for instance. More precisely, we prove that under some assumptions on the nonlinear term in a model of McKendrick-Von Foerster we deduce easily the global convergence using the General Relative Entropy (GRE) method of entropy. Then we compare the local asymptotic results obtained by linearisation and by the GRE principle.
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