Abstract We consider an Allen–Cahn equation with nonlinear diffusion, motivated by the
study of the scaling limit of certain interacting particle systems. We investigate its singular …

We derive a continuum mean-curvature flow as a certain hydrodynamic scaling limit of a
class of Glauber+ Zero-range particle systems. The Zero-range part moves particles while …

A logarithmic model type chemotaxis equation is introduced with porous medium diffusion
and a population dependent consumption rate. The classical assumption that individual …

We consider the nutrient–chemotaxis model, derived by a food metric, on the real line. The
model consists of the equation for the nutrient density of ordinary differential equation type …

We study a stochastic Allen-Cahn equation with nonlinear diffusion and a mild multiplicative
noise on a bounded domain in R n. We consider initial data which satisfy some non …

This paper deals with the nutrient-taxis system derived by a food metric. The system was
proposed in [Sun-Ho Choi and Yong-Jung Kim: Chemotactic traveling waves by metric of …

In a spatially heterogeneous environment the propagation speed of a biological invasion
varies in space. The traveling wave theory in a homogeneous case is not extended to a …

We consider an Allen-Cahn equation with nonlinear diffusion, motivated by the study of the
scaling limit of certain interacting particle systems. We investigate its singular limit and show …

Food metric diffusion is a non-autonomous operator which takes into account the effect of
spatial heterogeneity of resource distribution to biological migration. Its use in a …