On the Inverse Problem for a Size-Structured Population Model

Benoît Perthame (1, 2) , Jorge Zubelli (3)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 BANG - Nonlinear Analysis for Biology and Geophysical flows
3 IMPA - Instituto Nacional de Matemática Pura e Aplicada

We consider a size-structured model for cell division and address the question of determining the division (birth) rate from the measured stable size distribution of the population. We formulate such question as an inverse problem for an integro-differential equation posed on the half line. We develop firstly a regular dependency theory for the solution in terms of the coefficients and, secondly, a novel regularization technique for tackling this inverse problem which takes into account the specific nature of the equation. Our results rely also on generalized relative entropy estimates and related Poincaré inequalities.

Mots clés: Size structure models. Inverse problem. Regularization technique. Entropy methods; Size structure models. Inverse problem. Regularization technique. Entropy methods.

Domaines: Equations aux dérivées partielles [math.AP]

Benoît Perthame, Jorge Zubelli. On the Inverse Problem for a Size-Structured Population Model. 2006. ⟨hal-00110904⟩