- Path:
Periodical
- Title:
- Advances in nonlinear analysis
- Publication:
-
Berlin Boston, Mass.: de Gruyter
- Note:
- Gesehen am 18.03.2019
- Fortsetzung der Druck-Ausgabe
- Open Access
- Namensnennung 4.0 International
- Scope:
- Online-Ressource
- ISSN:
- 2191-950X
- ZDB-ID:
-
2645915-2
- VÖBB-Katalog:
- 15630346
- Keywords:
- Zeitschrift
- Classification:
- Mathematik
- Collection:
- Mathematik
- Copyright:
- Rights reserved
- Accessibility:
- Free Access
- Title:
- Advances in nonlinear analysis
- Publication:
-
Berlin Boston, Mass.: de Gruyter
- Note:
- Gesehen am 18.03.2019
- Fortsetzung der Druck-Ausgabe
- Open Access
- Namensnennung 4.0 International
- Scope:
- Online-Ressource
- ISSN:
- 2191-950X
- ZDB-ID:
-
2645915-2
- VÖBB-Katalog:
- 15630346
- Keywords:
- Zeitschrift
- Classification:
- Mathematik
- Collection:
- Mathematik
- Copyright:
- Rights reserved
- Accessibility:
- Free Access
Article
- Title:
- Solutions of stationary McKean–Vlasov equation on a high-dimensional sphere and other Riemannian manifolds
- Publication:
-
Berlin Boston, Mass.: de Gruyter, 2026
- Language:
- English
- Information:
- Abstract: We study stationary solutions of McKean–Vlasov equation on a high-dimensional sphere and other compact Riemannian manifolds. We extend the equivalence of the energetic problem formulation to the manifold setting and characterize critical points of the corresponding free energy functional. On a sphere, we employ the properties of spherical convolution to study the bifurcation branches around the uniform state. We also give a sufficient condition for an existence of a discontinuous transition point in terms of the interaction kernel and compare it to the Euclidean setting. We illustrate our results on a range of system, including the particle system arising from the transformer models and the Onsager model of liquid crystals.
- Scope:
- Online-Ressource
- Note:
- Open Access
- Archivierung/Langzeitarchivierung gewährleistet
- Keywords:
- McKean–Vlasov equation ; bifurcations ; phase transition ; nonlocal PDEs ; interacting particle systems ; PDEs on manifolds ; 35R01 ; 35A15 ; 35B32 ; 25B38 ; 35G20
- Classification:
- Mathematik
- Collection:
- Mathematik
- Copyright:
- CC BY
- Accessibility:
- Free Access
- Title:
- Solutions of stationary McKean–Vlasov equation on a high-dimensional sphere and other Riemannian manifolds
- Publication:
-
Berlin Boston, Mass.: de Gruyter, 2026
- Language:
- English
- Information:
- Abstract: We study stationary solutions of McKean–Vlasov equation on a high-dimensional sphere and other compact Riemannian manifolds. We extend the equivalence of the energetic problem formulation to the manifold setting and characterize critical points of the corresponding free energy functional. On a sphere, we employ the properties of spherical convolution to study the bifurcation branches around the uniform state. We also give a sufficient condition for an existence of a discontinuous transition point in terms of the interaction kernel and compare it to the Euclidean setting. We illustrate our results on a range of system, including the particle system arising from the transformer models and the Onsager model of liquid crystals.
- Scope:
- Online-Ressource
- Note:
- Open Access
- Archivierung/Langzeitarchivierung gewährleistet
- Keywords:
- McKean–Vlasov equation ; bifurcations ; phase transition ; nonlocal PDEs ; interacting particle systems ; PDEs on manifolds ; 35R01 ; 35A15 ; 35B32 ; 25B38 ; 35G20
- Classification:
- Mathematik
- Collection:
- Mathematik
- Copyright:
- CC BY
- Accessibility:
- Free Access
