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Microscopic derivation of degenerated diffusion phenomena

Abstract : This manuscript reviews a large part of my research work since the end of my PhD thesis, which has beenmostly directed towards the following demanding question: how can we derive various types of nonlinear partial differential equations (PDEs), observed at our macroscopic level, from the underlying microscopic particle systems via a suitably taken long time and large space scaling limit. The mathematical challenge consists in proving convergence theorems known as hydrodynamic limits, in order to recover the macroscopic PDEs given by physics. Typical examples of micro/macro description problems are heat conduction, fluid flow inside a physical medium or phase transitions in matter. With my coauthors we have analyzed several mathematical models which aimed at: understanding the microscopic features of anomalous diffusion; describing propagation effects in multiphase media as well as randomly growing interfaces. Two classes of one-dimensional models are mainly considered, they all have a stochastic component and follow at least one conservation rule: (1) kinetically constrained lattice gases which are subject to dynamics restrictions ; (2) Hamiltonian systems of atoms perturbed by a stochastic noise.
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https://hal.inria.fr/tel-02399713
Contributor : Marielle Simon <>
Submitted on : Tuesday, December 10, 2019 - 4:12:15 PM
Last modification on : Friday, April 3, 2020 - 3:06:03 PM
Document(s) archivé(s) le : Wednesday, March 11, 2020 - 1:22:17 PM

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Marielle Simon. Microscopic derivation of degenerated diffusion phenomena. Mathematics [math]. Université de Lille, 2019. ⟨tel-02399713⟩

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