Adaptive observer for age-structured population with spatial diffusion

Karim Ramdani (1, 2) , Julie Valein (1, 2) , Jean-Claude Vivalda (1, 2)

1 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization
2 IECL - Institut Élie Cartan de Lorraine

We investigate the inverse problem of simultaneously estimating the state and the spatial diffusion coefficient for an age-structured population model. The time evolution of the population is supposed to be known on a subdomain in space and age. We generalize to the infinite dimensional setting an adaptive observer originally proposed for finite dimensional systems.

Mots clés: Spatial diffusion; Inverse problems; Observer; Unknown parameter; Population dynamics

Domaines: Equations aux dérivées partielles [math.AP]

Karim Ramdani, Julie Valein, Jean-Claude Vivalda. Adaptive observer for age-structured population with spatial diffusion. North-Western European Journal of Mathematics, 2018, 4, pp.39-58. ⟨hal-01469488⟩