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4 papers
A Neural JKO Scheme for Hellinger-Kantorovich Gradient Flows via Monge-Growth Pairs
Geuntaek Seo, Cheolhyeong Kim, Hwijae Son +1
We develop a mesh-free neural JKO scheme for advection-reaction-diffusion equations with a gradient-flow structure in the Hellinger-Kantorovich (HK) geometry of unbalanced optimal…
Bounded weak solutions for Keller-Segel equations with generalized diffusion and logistic source via an unbalanced Optimal Transport splitting scheme
Kyungkeun Kang, Hwa Kil Kim, Geuntaek Seo
We consider a parabolic-elliptic type of Keller-Segel equations with generalized diffusion and logistic source under homogeneous Neumann-Neumann boundary conditions. We construct b…
A gradient flow for the porous medium equations with Dirichlet boundary conditions
Dongkwang Kim, Dowan Koo, Geuntaek Seo
We consider the gradient flow structure of the porous medium equations with non-negative constant Dirichlet boundary conditions. We construct weak solutions to the equations via th…
Uniqueness and characterization of local minimizers for the interaction energy with mildly repulsive potentials
Kyungkeun Kang, Hwa Kil Kim, Tongseok Lim +1
In this paper, we are concerned with local minimizers of an interaction energy governed by repulsive-attractive potentials of power-law type in one dimension. We prove that sum of…