On the variations of the principal eigenvalue with respect to a   parameter in growth-fragmentation models
  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. 
Fabien Campillo (MATHNEURO, IMAG), Nicolas Champagnat (IECL, TOSCA),   Coralie Fritsch (CMAP, IECL, TOSCA)
math.AP math.PR