5 citations · 10 across the 10 of their papers we have counts for
10 papers
Fick's las selects the Neumann boundary condition
Danielle Hilhorst, Seung-Min Kang, Ho-Youn Kim +1
We study the appearance of a boundary condition along an interface between two regions, one with constant diffusivity and the other with diffusivity $\eps>0$, when $\eps\to0$.…
Diffusion laws select boundary conditions
Jaywan Chung, Seungmin Kang, Ho-Youn Kim +1
The choice of boundary condition makes an essential difference in the solution structure of diffusion equations. The Dirichlet and Neumann boundary conditions and their combination…
Random walk with heterogeneous sojourn time
Jaywan Chung, Yong-Jung Kim, Min-Gi Lee
We introduce a discrete-time random walk model on a one-dimensional lattice with a nonconstant sojourn time and prove that the discrete density converges to a solution of a continu…
Terrace solutions for non-Lipschitz multistable nonlinearities
Thomas Giletti, Ho-Youn Kim, Yong-Jung Kim
Traveling wave solutions of reaction-diffusion equations are well-studied for Lipschitz continuous monostable and bistable reaction functions. These special solutions play a key ro…
On the modelling of spatially heterogeneous nonlocal diffusion: deciding factors and preferential position of individuals
Matthieu Alfaro, Thomas Giletti, Yong-Jung Kim +2
We develop general heterogeneous nonlocal diffusion models and investigate their connection to local diffusion models by taking a singular limit of focusing kernels. We reveal the…
Evolution of dietary diversity and a starvation driven cross-diffusion system as its singular limit
Elisabetta Brocchieri, Lucilla Corrias, Helge Dietert +1
We rigorously prove the passage from a Lotka-Volterra reaction-diffusion system towards a cross-diffusion system at the fast reaction limit. The system models a competition of two…
Bacterial chemotaxis without gradient-sensing
Changwook Yoon, Yong-Jung Kim
Models for chemotaxis are based on gradient sensing of individual organisms. The key contribution of Keller and Segel is showing that erratic movements of individuals may result in…
Einstein's random walk and thermal diffusion
Yong-Jung Kim
Thermal diffusion has been studied for over 150 years. Despite of the long history and the increasing importance of the phenomenon, the physics of thermal diffusion remains poorly…
Structure of the fundamental solution of a nonconvex conservation law
Yong-Jung Kim, Young-Ran Lee
The structure of a signed fundamental solution of a conservation law is studied without the convexity assumption. The types of shocks and rarefaction waves are classified together…
A geometric one-sided inequality for zero-viscosity limits
Yong-Jung Kim
The Oleinik inequality for conservation laws and Aronson-Benilan type inequalities for porous medium or p-Laplacian equations are one-sided inequalities that provide the fundamenta…