Long-Time Asymptotics of Kinetic Models of Granular Flows

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Lp theory for the multidimensional aggregation equation (2011, background): “3) arises in a number of models for biological aggregation [11, 14, 15, 23, 28, 37, 36, 38, 39] as well as problems in materials science [24, 25] and granular media [3, 17, 18, 31, 40].”
Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations (2011, methodology): “Simplified inelastic interaction models for granular media were considered in [4] [18] with W = |x| 3 /3 and [43] [28] with W = |x| α , α > 1.”
Stationary states of quadratic diffusion equations with long-range attraction (2011, background): “In the purely nonlocal case, namely when ε = 0, this issue has been studied extensively in many papers [37, 13, 35, 5, 4, 16, 6, 7, 29, 25, 24], combined with the study of the regularity of solutions compared to the attractive singularity of the interaction kernel.”
Blow-up in multidimensional aggregation equations with mildly singular interaction kernels (2009, methodology): “This class of equations belongs to the same family of nonlinear friction equations that appear in the modelling of granular media [4, 15, 16, 27, 37].”
Contractions in the 2-Wasserstein Length Space and Thermalization of Granular Media (2006, background): “Let us also mention that Wasserstein contraction estimates have been obtained recently by Li & Toscani [37] for the family of one dimensional granular media models introduced in [51].”