On an aggregation model with long and short range interactions

By Martin Burger, V. Capasso, D. Morale. 2007

186 citations recorded by the source corpus.

Subfields: Global and Planetary Change, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/b3bcdf9282659ed3fe69152d2780cf08259a1ca8

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In Global and Planetary Change

In Modeling and Simulation

In Public Health, Environmental and Occupational Health

Citations in the corpus

Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations (2011, methodology): “Mathematical modeling of the collective behavior of individuals, such as swarming, has also been treated by continuum models steaming from discrete particle models [33, 14, 41, 34, 42, 15, 36, 13, 21, 23, 16, 17].”
Finite-Time Blow-up of Solutions of an Aggregation Equation in Rn (2007, background): “Burger and collaborators [5, 4 ] consider well-posedness of the model with an additional ‘porous media’ type smoothing term.”
Long-Time Behaviour and Phase Transitions for the Mckean–Vlasov Equation on the Torus (2018, background): “Systems of interacting particles arise in a myriad of applications ranging from opinion dynamics [41], granular materials [6,11,25] and mathematical biology [8,47] to statistical mechanics [50], galactic dynamics [18], droplet growth [29], plasma physics [14], and synchronisation [48].”
Finite-time blow-up of L∞-weak solutions of an aggregation equation (2010, background): “1), with the addition of a densitydependent diffusion used to model repulsion, were studied in [6] for initial data u0∈ L(1)(R)∩L(R) also satisfying u(2)0∈H (1)(R).”
On minimizers of interaction functionals with competing attractive and repulsive potentials (2015, unknown): “[7, 8, 14, 17, 20, 21, 22, 23]).”
Stationary states of quadratic diffusion equations with long-range attraction (2011, background): “existence and uniqueness in the context of entropy solutions [12, 8], well-posedness in the context of Wasserstein gradient flows as a special case of the theory developed in [1], and - in particular in connection with the classical Patlak-Keller-Segel model for chemotaxis [47, 32] - with respect to”
Local and Global Existence for an Aggregation Equation (2007, background): “We also note that Burger et al. (2007) prove well-posedness of an equation similar to (1.1) in n space dimensions when the potential G is C1.”
Particle, kinetic, and hydrodynamic models of swarming (2010, unknown): “Some continuum models were derived phenomenologically [10, 63–65] including attraction–repulsion mechanisms through a mean force and spatial diffusion to deal with the anticrowding tendency.”
Local and global well-posedness for aggregation equations and Patlak–Keller–Segel models with degenerate diffusion (2010, background): “Classically, linear diffusion is used, however recently, there has been a widening interest in models with degenerate diffusion to include over-crowding effects [60, 17].”
Stochastic Mean-Field Limit: Non-Lipschitz Forces & Swarming (2010, background): “We also refer to [31, 7] for related problems and biological discussions in space-homogeneous kinetic models with globally Lipschitz drifts but nonlinear diffusions.”
Double milling in self-propelled swarms from kinetic theory (2009, background): “While several continuum models based on heuristic derivations have been presented in the literature, few attempts have been made at deriving such models starting from principles of dynamics of individual agents [5, 9, 20, 13, 14].”