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Updated: Jun 20, 2025

Combining Fluidic Devices with Microscopy and Flow Cytometry to Study Microbial Transport in Porous Media Across Spatial Scales
Published on: November 25, 2020
Biological invasion with a porous medium type diffusion in a heterogeneous space
Hyunjoon Park1, Yong-Jung Kim2
1Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Nakano, Nakano-ku, Tokyo, 164-8525, Japan.
Abstract:
The knowledge of traveling wave solutions is the main tool in the study of wave propagation. However, in a spatially heterogeneous environment, traveling wave solutions do not exist, and a different approach is needed. In this paper, we study the generation and the propagation of hyperbolic scale singular limits of a KPP-type reaction-diffusion equation when the carrying capacity is spatially heterogeneous and the diffusion is of a porous medium equation type. We show that the interface propagation speed varies according to the carrying capacity.
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