Related papers: Global minimizers for fast diffusion versus nonloc…
We consider a free energy functional on Cartan-Hadamard manifolds, and investigate the existence of its global minimizers. The energy functional consists of two components: an entropy (or internal energy) and an interaction energy modelled…
We investigate the ground states of a free energy functional on sphere. The energy consists of an entropy and a nonlocal interaction term that are in competition with each other, as they favour spreading and aggregation, respectively.…
We consider a free energy on the sphere that contains an entropy associated to nonlinear fast diffusion, and a nonlocal interaction energy. The two components of the free energy compete with each other, as one favours spreading and the…
We investigate a free energy functional that arises in aggregation-diffusion phenomena modelled by nonlocal interactions and local repulsion on the hyperbolic space $\bbh^\dm$. The free energy consists of two competing terms: an entropy,…
We consider an aggregation-diffusion energy on Cartan-Hadamard manifolds with sectional curvatures that can grow unbounded at infinity. The energy corresponds to a macroscopic aggregation model that involves nonlocal interactions and linear…
We analyze free energy functionals for macroscopic models of multi-agent systems interacting via pairwise attractive forces and localized repulsion. The repulsion at the level of the continuous description is modeled by pressure-related…
We investigate which nonlocal-interaction energies have a ground state (global minimizer). We consider this question over the space of probability measures and establish a sharp condition for the existence of ground states. We show that…
We consider a free energy functional defined on probability densities on the unit sphere $\mathbb{S}^d$, and investigate its global minimizers. The energy consists of two components: an entropy and a nonlocal interaction energy, which…
We prove the existence of non-trivial global minimizers of a class of free energies related to aggregation equations with degenerate diffusion on $\Real^d$. Such equations arise in mathematical biology as models for organism group dynamics…
We study global minimizers of a functional modeling the free energy of thin liquid layers over a solid substrate under the combined effect of surface, gravitational, and intermolecular potentials. When the latter ones have a mild repulsive…
We investigate stationary solutions of a non-local aggregation equation with degenerate power-law diffusion and bounded attractive potential in arbitrary dimensions. Compact stationary solutions are characterized and compactness…
This paper is concerned with the macroscopic behavior of global energy minimizers in the three-dimensional sharp interface unscreened Ohta-Kawasaki model of diblock copolymer melts. This model is also referred to as the nuclear liquid drop…
We consider macroscopic descriptions of particles where repulsion is modelled by non-linear power-law diffusion and attraction by a homogeneous singular kernel leading to variants of the Keller-Segel model of chemotaxis. We analyse the…
We investigate the effect of linear diffusion and interactions with the domain boundary on swarm equilibria by analyzing critical points of the associated energy functional. Through this process we uncover two properties of energy…
We consider the minimisation of power-law repulsive-attractive interaction energies which occur in many biological and physical situations. We show existence of global minimizers in the discrete setting and get bounds for their supports…
The existence of compactly supported global minimisers for continuum models of particles interacting through a potential is shown under almost optimal hypotheses. The main assumption on the potential is that it is catastrophic, or not…
This paper investigates the existence and qualitative properties of minimizers for a class of nonlocal micromagnetic energy functionals defined on bounded domains. The considered energy functional consists of a symmetric exchange…
Existence and regularity of minimizers for a geometric variational problem is shown. The variational integral models an energy contribution of the interface between two immiscible fluids in the presence of surfactants and includes a…
We consider a finite region of a lattice of weakly interacting geodesic flows on manifolds of negative curvature and we show that, when rescaling the interactions and the time appropriately, the energies of the flows evolve according to a…
In this paper we consider minimizers for nonlocal energy functionals generalizing elastic energies that are connected with the theory of peridynamics \cite{Silling2000} or nonlocal diffusion models \cite{Rossi}. We derive nonlocal versions…