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Issue ESAIM: Proc.
Volume 25, 2008
Paris-sud working group on modelling and scientific computing 2007-2008
Page(s) 29 - 43
DOI http://dx.doi.org/10.1051/proc:082503
Published online 16 January 2009

ESAIM: Proc., 2008, Vol. 25, pp. 29-43
DOI: 10.1051/proc:082503

Well-posedness of an epidemiological problem described by an evolution PDE

A. Perasso1, 2 and B. Laroche2

1  Laboratoire de Mathématiques, Bâtiment 425, Université Paris-Sud XI, F-91405 Orsay Cedex, France.
2  Laboratoire des signaux et systèmes (L2S) Supélec - 3 rue Joliot-Curie 91192 Gif-sur-Yvette cedex, France.


Published online: 16 January 2009

Abstract
This paper investigates the well-posedness for a non linear transport equation system that models the spread of prion diseases in a managed flock. Existence and uniqueness of solutions are proved with the use of semigroup theory in the case of a Lipschitz perturbation and presence of boundary conditions. Finally, the characteristics of the transport part of the equations allow us to give an implicit expression of the solution.


Résumé
Dans ce papier, nous établissons le caractère bien posé d'un problème de transport non linéaire modélisant la propagation d'une maladie à prion dans un troupeau expérimental. Nous prouvons existence et unicité de la solution du problème à l'aide de la théorie des semigroupes, avec présence de conditions de bord et une partie non linéaire localement lipschitzienne. Nous donnons pour conclure une expression implicite de la solution utilisant les caractéristiques des équations de transport.



© EDP Sciences, ESAIM 2008


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