69 citations · 196 across the 30 of their papers we have counts for
32 papers
Stability of equilibria of an aggregation-diffusion energy on sphere
Razvan C. Fetecau, Hansol Park
We consider an aggregation-diffusion energy on the sphere and investigate the stability of its equilibria. The energy consists of a porous-medium type nonlinear entropy $\frac{1}{m…
Ground states and phase transitions for an aggregation model with fast diffusion on sphere
Razvan C. Fetecau, Hansol Park
We consider a free energy on the sphere that contains an entropy associated to nonlinear fast diffusion, and a nonlocal interaction energy. The two components of the free energy co…
Numerical approximation of the first -Laplace eigenpair
Hannah Potgieter, Razvan C. Fetecau, Steven J. Ruuth
We approximate the first Dirichlet eigenpair of the -Laplace operator for on both Euclidean and surface domains. We emphasize large values and discuss ho…
Global energy minimizers for a diffusion-aggregation model on sphere
Razvan C. Fetecau, Hansol Park, Vishnu Vaidya
We investigate the ground states of a free energy functional on sphere. The energy consists of an entropy and a nonlocal interaction term that are in competition with each other, a…
Geodesic distance approximation using a surface finite element method for the -Laplacian
Hannah Potgieter, Razvan C. Fetecau, Steven J. Ruuth
We use the -Laplacian with large -values in order to approximate geodesic distances to features on surfaces. This differs from Fayolle and Belyaev's (2018) [1] computational…
Global minimizers for fast diffusion versus nonlocal interactions on negatively curved manifolds
José A. Carrillo, Razvan C. Fetecau, Hansol Park
We investigate the existence of ground states for a free energy functional on Cartan-Hadamard manifolds. The energy, which consists of an entropy and an interaction term, is associ…
Bifurcation of global energy minimizers for a diffusion-aggregation model on sphere
Razvan C. Fetecau, Hansol Park, Vishnu Vaidya
We consider a free energy functional defined on probability densities on the unit sphere , and investigate its global minimizers. The energy consists of two component…
Existence of ground states for free energies on the hyperbolic space
José A. Carrillo, Razvan C. Fetecau, Hansol Park
We investigate a free energy functional that arises in aggregation-diffusion phenomena modelled by nonlocal interactions and local repulsion on the hyperbolic space $\bbh^\dm$. The…
Ground states for aggregation-diffusion models on Cartan-Hadamard manifolds
Razvan C. Fetecau, Hansol Park
We consider a free energy functional on Cartan-Hadamard manifolds, and investigate the existence of its global minimizers. The energy functional consists of two components: an entr…
Aggregation-diffusion energies on Cartan-Hadamard manifolds of unbounded curvature
Razvan C. Fetecau, Hansol Park
We consider an aggregation-diffusion energy on Cartan-Hadamard manifolds with sectional curvatures that can grow unbounded at infinity. The energy corresponds to a macroscopic aggr…
Swarming models with specular boundary condition and environmental noise
Razvan C. Fetecau, Hui Huang, Jinniao Qiu
We investigate a general class of models for swarming/self-collective behaviour in domains with boundaries. The model is expressed as a stochastic system of interacting particles s…
Long-time behaviour of interaction models on Riemannian manifolds with bounded curvature
Razvan C. Fetecau, Hansol Park
We investigate the long-time behaviour of solutions to a nonlocal partial differential equation on smooth Riemannian manifolds of bounded sectional curvature. The equation models s…
Equilibria and energy minimizers for an interaction model on the hyperbolic space
Razvan C. Fetecau, Hansol Park
We study an intrinsic model for collective behaviour on the hyperbolic space $\bbh^\dm$. We investigate the equilibria of the aggregation equation (or equivalently, the critical po…
Well-posedness of an interaction model on Riemannian manifolds
Razvan C. Fetecau, Francesco S. Patacchini
We investigate a model for collective behaviour with intrinsic interactions on smooth Riemannian manifolds. For regular interaction potentials, we establish the local well-posednes…
Emergent behaviors of rotation matrix flocks
Razvan C. Fetecau, Seung-Yeal Ha, Hansol Park
We derive an explicit form for the Cucker-Smale (CS) model on the special orthogonal group by identifying closed form expressions for geometric quantities such as…
Safe Coverage of Moving Domains for Vehicles with Second Order Dynamics
Juan Chacon, Mo Chen, Razvan Fetecau
Autonomous coverage of a specified area by robots operating in close proximity with each other has many potential applications such as real-time monitoring of rapidly changing envi…
An intrinsic aggregation model on the special orthogonal group : well-posedness and collective behaviours
Razvan C. Fetecau, Seung-Yeal Ha, Hansol Park
We investigate an aggregation model with intrinsic interactions on the special orthogonal group . We consider a smooth interaction potential that depends on the squared intr…
Safe Coverage of Compact Domains For Second Order Dynamical Systems
Juan Chacon, Mo Chen, Razvan C. Fetecau
Autonomous systems operating in close proximity with each other to cover a specified area has many potential applications, but to achieve effective coordination, two key challenges…
Equilibria of an aggregation model with linear diffusion in domains with boundaries
Daniel A. Messenger, Razvan C. Fetecau
We investigate the effect of linear diffusion and interactions with the domain boundary on swarm equilibria by analyzing critical points of the associated energy functional. Throug…
Zero-diffusion Limit for Aggregation Equations over Bounded Domains
Razvan C. Fetecau, Hui Huang, Daniel Messenger +1
We establish the zero-diffusion limit for both continuous and discrete aggregation models over convex and bounded domains. Compared with a similar zero-diffusion limit derived in […
Propagation of chaos for the Keller-Segel equation over bounded domains
Razvan C. Fetecau, Hui Huang, Weiran Sun
In this paper we rigorously justify the propagation of chaos for the parabolic-elliptic Keller-Segel equation over bounded convex domains. The boundary condition under consideratio…
Self-organization on Riemannian manifolds
Razvan C. Fetecau, Beril Zhang
We consider an aggregation model that consists of an active transport equation for the macroscopic population density, where the velocity has a nonlocal functional dependence on th…
Swarming in domains with boundaries: approximation and regularization by nonlinear diffusion
Razvan C. Fetecau, Mitchell Kovacic, Ihsan Topaloglu
We consider an aggregation model with nonlinear diffusion in domains with boundaries and investigate the zero diffusion limit of its solutions. We establish the convergence of weak…
Equilibria for an aggregation model with two species
Joep H. M. Evers, Razvan C. Fetecau, Theodore Kolokolnikov
We consider an aggregation model for two interacting species. The coupling between the species is via their velocities, that incorporate self- and cross-interactions. Our main inte…