2 papers
math.AP2025
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…
math.AP2024
Global boundedness and blow-up in a repulsive chemotaxis-consumption system in higher dimensions
Jaewook Ahn, Kyungkeun Kang, Dongkwang Kim
This paper investigates the repulsive chemotaxis-consumption model \begin{align*} \partial_t u &= \nabla \cdot (D(u) \nabla u) + \nabla \cdot (u \nabla v), \\ 0 &= Îv - uv \end{al…