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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 &= Δv - uv \end{ali…
math.AP2022
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…