Geodesically convex energies and confinement of solutions for a multi-component system of nonlocal interaction equations
DOI10.1007/s00030-016-0399-5zbMath1353.35299arXiv1412.3266OpenAlexW2963348507MaRDI QIDQ503119
Publication date: 11 January 2017
Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1412.3266
gradient flowinteraction potentialWasserstein distancegeodesic convexitymulti-species systemnonlocal evolution equation
Asymptotic behavior of solutions to PDEs (35B40) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Integro-partial differential equations (35R09)
Related Items (1)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Equivalence between duality and gradient flow solutions for one-dimensional aggregation equations
- A nonlocal continuum model for biological aggregation
- Existence and uniqueness of measure solutions for a system of continuity equations with non-local flow
- Nonlocal interaction equations: Stationary states and stability analysis.
- Confinement for repulsive-attractive kernels
- Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations
- Stability of stationary states of non-local equations with singular interaction potentials
- Confinement in nonlocal interaction equations
- Functional inequalities, thick tails and asymptotics for the critical mass Patlak-Keller-Segel model
- Contractions in the 2-Wasserstein length space and thermalization of granular media
- An integro-differential equation arising as a limit of individual cell-based models
- A proof of crystallization in two dimensions
- Kinetic models of opinion formation
- The Filippov characteristic flow for the aggregation equation with mildly singular potentials
- Finite-time blow-up of \(L^\infty \)-weak solutions of an aggregation equation
- Double milling in self-propelled swarms from kinetic theory
- Large time behavior of nonlocal aggregation models with nonlinear diffusion
- An integro-differential equation model for alignment and orientational aggregation
- A non-local model for a swarm
- A convexity principle for interacting gases
- An interacting particle system modelling aggregation behavior: from individuals to populations
- Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
- Long-time asymptotics of kinetic models of granular flows
- Nonlocal crowd dynamics models for several populations
- Measure valued solutions of the 2D Keller-Segel system
- Existence of compactly supported global minimisers for the interaction energy
- Gradient flows for non-smooth interaction potentials
- Singular patterns for an aggregation model with a confining potential
- Finite-time blow-up of solutions of an aggregation equation in \(\mathbb R^n\)
- On an aggregation model with long and short range interactions
- One-dimensional kinetic models of granular flows
- THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
- A nonlocal swarm model for predators–prey interactions
- Measure solutions for non-local interaction PDEs with two species
- Stability and clustering of self-similar solutions of aggregation equations
- A WELL-POSEDNESS THEORY IN MEASURES FOR SOME KINETIC MODELS OF COLLECTIVE MOTION
- Lp theory for the multidimensional aggregation equation
- STABLE STATIONARY STATES OF NON-LOCAL INTERACTION EQUATIONS
- Blow-up in multidimensional aggregation equations with mildly singular interaction kernels
- Blowup of solutions to a diffusive aggregation model
- A kinetic equation for granular media
- The Variational Formulation of the Fokker--Planck Equation
- Macroscopic evolution of particle systems with short- and long-range interactions
- Swarming Patterns in a Two-Dimensional Kinematic Model for Biological Groups
- Equivalence of gradient flows and entropy solutions for singular nonlocal interaction equations in 1D
- Ground States for Diffusion Dominated Free Energies with Logarithmic Interaction
- Local and Global Existence for an Aggregation Equation
- Transport distances and geodesic convexity for systems of degenerate diffusion equations
This page was built for publication: Geodesically convex energies and confinement of solutions for a multi-component system of nonlocal interaction equations