5 papers · 1 filter
Gradient Flow Structure of the Spontaneous Aggregation Model
Jan Haskovec
We identify a previously unnoticed gradient-flow structure of the Fokker--Planck equation arising in the spontaneous particle aggregation model. For an exponential response functio…
Memory Stabilizes Spontaneous Particle Aggregation: A Linearized Vlasov--Fokker--Planck Analysis
Jan Haskovec
We perform a linearized stability analysis of the Vlasov--Fokker--Planck equation obtained as the mean-field description of a stochastic spontaneous aggregation model with memory.…
High-friction limit for bipolar Euler-Riesz systems
Nuno J. Alves, Jan Haskovec
We consider a bipolar Euler-Riesz system and rigorously justify the high-friction limit of weak solutions towards a bipolar aggregation-diffusion system with Riesz interactions. Th…
Gradient Flows for the -Laplacian Arising from Biological Network Models: A Novel Dynamical Relaxation Approach
Jan Haskovec, Peter Markowich, Stefano Zampini
We investigate a scalar partial differential equation model for the formation of biological transportation networks. Starting from a discrete graph-based formulation on equilateral…
Measure-based approach to mesoscopic modeling of optimal transportation networks
Jan Haskovec, Peter Markowich, Simone Portaro
We propose a mesoscopic modeling framework for optimal transportation networks with biological applications. The network is described in terms of a joint probability measure on the…