Long-time Asymptotics for Nonlinear Growth-fragmentation Equations
Analysis of PDEs
2019-02-28 v2
Abstract
We are interested in the long-time asymptotic behavior of growth-fragmentation equations with a nonlinear growth term. We present examples for which we can prove either the convergence to a steady state or conversely the existence of periodic solutions. Thanks the General Relative Entropy method applied to well chosen self-similar solutions, we show that the equation can "asymptotically" be reduced to a system of ODEs. Then stability results are proved by using a Lyapunov functional, and existence of periodic solutions are proved thanks to the Poincar\'e-Bendixon theorem or by Hopf bifurcation.
Cite
@article{arxiv.1102.2871,
title = {Long-time Asymptotics for Nonlinear Growth-fragmentation Equations},
author = {Pierre Gabriel},
journal= {arXiv preprint arXiv:1102.2871},
year = {2019}
}