On the derivation of non-local diffusion equations in confined spaces
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Abstract
The subject of the thesis is the derivation of non-local diffusion equations from kinetic models with heavy-tailed equilibrium in velocity. We are particularly interested in confining the kinetic equations and developing methods that allow us, from the confined kinetic models, to derive confined versions of non-local diffusion equations.
Description
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Advisors
Mouhot, Clément
Keywords
Kinetic theory of gases, Diffusion processes, Diffusion limits, Analysis of PDEs, Vlasov-Fokker-Planck equations, Fractional Laplacian, Vlasov equations
Qualification
Doctor of Philosophy (PhD)
Awarding Institution
University of Cambridge
Sponsorship
European Research Council Grant ERC-2011-StG Mathematical Topics of Kinetic Theory