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Biological invasion with a porous medium type diffusion in a heterogeneous space.

Hyunjoon ParkYong-Jung Kim
Published in: Journal of mathematical biology (2024)
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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