Nonlocal interaction equations: Stationary states and stability analysis.

zbMath1265.35142MaRDI QIDQ454525

Gaël Raoul

Publication date: 8 October 2012

Published in: Differential and Integral Equations (Search for Journal in Brave)

zbMATH Keywords

asymptotic behaviorinteraction potentialexternal potentialDirac mass

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Perturbations in context of PDEs (35B20) PDEs in connection with classical thermodynamics and heat transfer (35Q79)

Related Items (14)

Regularity of local minimizers of the interaction energy via obstacle problems ⋮ Turing and Turing-Hopf bifurcations for a reaction diffusion equation with nonlocal advection ⋮ On the necessary optimality conditions for the fractional Cucker-Smale optimal control problem ⋮ Convergence of a linearly transformed particle method for aggregation equations ⋮ Asymptotic behavior of a nonlocal advection system with two populations ⋮ Dimensionality of local minimizers of the interaction energy ⋮ An anisotropic interaction model for simulating fingerprints ⋮ A one-dimensional logistic like equation with nonlinear and nonlocal diffusion: strong convergence to equilibrium ⋮ Pattern formation of a nonlocal, anisotropic interaction model ⋮ Geodesically convex energies and confinement of solutions for a multi-component system of nonlocal interaction equations ⋮ A blob method for the aggregation equation ⋮ Stability Analysis of Line Patterns of an Anisotropic Interaction Model ⋮ Particle, kinetic, and hydrodynamic models of swarming ⋮ Existence of compactly supported global minimisers for the interaction energy

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