Nonlocal Interaction Equations in Environments with Heterogeneities and Boundaries

DOI10.1080/03605302.2015.1015033zbMath1327.35057OpenAlexW1966710059MaRDI QIDQ3448231

Lijiang Wu, Dejan Slepčev

Publication date: 23 October 2015

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605302.2015.1015033

zbMATH Keywords

optimal transportgradient flowsparticle approximationwell-posedness of measure solutionsequations on manifoldsRiemannian 2-Wasserstein metric

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Integro-partial differential equations (45K05) Weak solutions to PDEs (35D30) Animal behavior (92D50)

Related Items (17)

Swarm Equilibria in Domains with Boundaries ⋮ Swarming in domains with boundaries: approximation and regularization by nonlinear diffusion ⋮ Optimal measures for \(p\)-frame energies on spheres ⋮ On continuity equations in space-time domains ⋮ Zero-diffusion limit for aggregation equations over bounded domains ⋮ Long-time behaviour of interaction models on Riemannian manifolds with bounded curvature ⋮ Equilibria and energy minimizers for an interaction model on the hyperbolic space ⋮ Pattern formation of a nonlocal, anisotropic interaction model ⋮ Well-posedness of an interaction model on Riemannian manifolds ⋮ Equilibria of an aggregation model with linear diffusion in domains with boundaries ⋮ Energy on spheres and discreteness of minimizing measures ⋮ Nonlocal adhesion models for two cancer cell phenotypes in a multidimensional bounded domain ⋮ An intrinsic aggregation model on the special orthogonal group \(SO(3)\): well-posedness and collective behaviours ⋮ Nonlocal Adhesion Models for Microorganisms on Bounded Domains ⋮ The nonlocal-interaction equation near attracting manifolds ⋮ Well-posedness and asymptotic behavior of an aggregation model with intrinsic interactions on sphere and other manifolds ⋮ Nonlocal-interaction equations on uniformly prox-regular sets

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