Confinement in nonlocal interaction equations

DOI10.1016/j.na.2011.08.057zbMath1233.35032OpenAlexW2041440299WikidataQ112632013 ScholiaQ112632013MaRDI QIDQ651127

Juan-Miguel Gracia

Publication date: 8 December 2011

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: http://opus.bath.ac.uk/32318/1/confinement_final.pdf

zbMATH Keywords

gradient flowsparticle approximationattractive at long distancescontinuum descriptionslocalized configurationrepulsive at short distances

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Asymptotic behavior of solutions to PDEs (35B40) Integro-partial differential equations (45K05) Initial value problems for linear first-order PDEs (35F10) Genetics and population dynamics (92Dxx)

Related Items (19)

Regularity of local minimizers of the interaction energy via obstacle problems ⋮ Nonlocal Interaction Equations in Environments with Heterogeneities and Boundaries ⋮ Convergence of a linearly transformed particle method for aggregation equations ⋮ Dimensionality of local minimizers of the interaction energy ⋮ An anisotropic interaction model for simulating fingerprints ⋮ On global minimizers of repulsive–attractive power-law interaction energies ⋮ Some free boundary problems involving non-local diffusion and aggregation ⋮ On minimizers of interaction functionals with competing attractive and repulsive potentials ⋮ Pattern formation of a nonlocal, anisotropic interaction model ⋮ Gradient flows for non-smooth interaction potentials ⋮ Nonlocal interactions by repulsive-attractive potentials: radial ins/stability ⋮ Confinement for repulsive-attractive kernels ⋮ Geodesically convex energies and confinement of solutions for a multi-component system of nonlocal interaction equations ⋮ Sharp discontinuous traveling waves in a hyperbolic Keller–Segel equation ⋮ A blob method for the aggregation equation ⋮ Existence and uniqueness of solutions for a hyperbolic Keller-Segel equation ⋮ The exponential formula for the wasserstein metric ⋮ Stability Analysis of Line Patterns of an Anisotropic Interaction Model ⋮ Existence of ground states of nonlocal-interaction energies

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