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Theses

Application du calcul stochastique à une classe d'EDP non linéaire

Abstract : In this thesis, we used the tools of stochastic calculation for
to obtain the existence and the unicity of the solution of a PDE of
non-linear whose origin goes up being studied of the models of sticking particles.
Firstly, one builds two diffusions directed by Brownian independent exits of different points but whose drift is the same function which combines the two densities of the one and the other diffusions. It is shown that the good combination of the density and the speed of the particles is solution of a system of partial derivative equations called gas system without pressure with viscosity.
Secondly, One takes again the problems of an article of Sheu on the densities of transition from a diffusion not degenerated, one leads to a better precision on the constants appearing in the estimate of Sheu.
Finally, one generalizes the gas system without pressure already studied by A. Dermoune in 2003, by replacing the Laplacian by an operator more general. Then one shows: the existence of a weak solution for a nonlinear differential equation stochastic, identification of the drift and the unicity of the solution.
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Submitted on : Thursday, March 23, 2006 - 4:33:39 PM
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Siham Filali. Application du calcul stochastique à une classe d'EDP non linéaire. Mathématiques [math]. Université des Sciences et Technologie de Lille - Lille I, 2005. Français. ⟨tel-00012025⟩

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