Communications in Mathematical Sciences
Volume 15 (2017)
On the variations of the principal eigenvalue with respect to a parameter in growth-fragmentation models
Pages: 1801 – 1819
We study the variations of the principal eigenvalue associated to a growth-fragmentation-death equation with respect to a parameter acting on growth and fragmentation. To this aim, we use the probabilistic individual-based interpretation of the model. We study the variations of the survival probability of the stochastic model using a generation by generation approach. Then, making use of the link between the survival probability and the principal eigenvalue established in a previous work, we deduce the variations of the eigenvalue with respect to the parameter of the model.
growth-fragmentation model, eigenproblem, integro-differential equation, invasion fitness, individual-based model, infinite dimensional branching process, piecewise-deterministic Markov process, bacterial population
2010 Mathematics Subject Classification
35Q92, 45C05, 60J25, 60J80, 60J85, 92D25
Paper received on 1 February 2016.
Paper accepted on 25 February 2017.