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Équations de transport-fragmentation et applications aux maladies à prions

Abstract : Growth and fragmentation of polymers play a central role in the development of prion diseases. To study these phenomena, we use the formalism of structured populations and analyze the integro-differential transport-fragmentation equation. First we investigate the eigenvalue problem for the linear transport-fragmentation operator. We prove existence and uniqueness of the principal eigenvalue and the associated eigenvectors under general conditions including the degenerate cases where the transport term can vanish at zero. Then we investigate the dependence of these eigenelements on the parameters of the equation and show existence of non-monotonic behaviors. The results allow us to address two different types of problems. The dependence on the transport term is used to find the steady states and to investigate the long time behavior of nonlinear models, including the "prion system". The dependence on the fragmentation term allows us to study an optimization problem. This means introducing a control on the fragmentation term and finding, for diagnostic purposes, the strategy which maximizes the growth of the population. In the last chapter, we present a conservative numerical scheme for aggregation-fragmentation equations including a coagulation term.
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Contributor : Pierre Gabriel Connect in order to contact the contributor
Submitted on : Monday, October 24, 2011 - 8:35:39 PM
Last modification on : Sunday, June 26, 2022 - 5:34:24 AM
Long-term archiving on: : Thursday, November 15, 2012 - 10:25:39 AM


  • HAL Id : tel-00635281, version 1


Pierre Gabriel. Équations de transport-fragmentation et applications aux maladies à prions. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2011. Français. ⟨tel-00635281⟩



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