Journal
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Volume 48, Issue 4, Pages 2806-2818Publisher
SIAM PUBLICATIONS
DOI: 10.1137/15M1045387
Keywords
fractional diffusion; kinetic transport models; macroscopic limit
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Funding
- PhD program Dissipation and Dispersion in Nonlinear PDEs - Austrian Science Fund [W1245]
- Vienna Science and Technology Fund [LS13-029]
- Consejo Nacional de Ciencia y Tecnologia
- beta complemento program of Secreteria de Education Publica, Mexico
- Austrian Science Fund (FWF) [W1245] Funding Source: Austrian Science Fund (FWF)
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A fractional diffusion equation with advection term is rigorously derived from a kinetic transport model with a linear turning operator, featuring a fat-tailed equilibrium distribution and a small directional bias due to a given vector field. The analysis is based on bounds derived by relative entropy inequalities and on two recently developed approaches for the macroscopic limit: a Fourier-Laplace transform method for spatially homogeneous data and the so called moment method, based on a modified test function.
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