Year: 2026
Type: article
Abstract: We consider the dynamics of an idealized cross-diffusion model of biological invasion in which the diffusion of an invading population is inhibited by a resident population, which is in turn degraded by the former. We formulate and numerically solve the problem that describes the self-similar smoothing of an initially piecewise-constant invading population. In the limit, the height ahead of the initial discontinuity vanishes and the speed of propagation also vanishes, but only logarithmically slowly. This result is confirmed by a matched asymptotic analysis. The singular nature of this limit indicates that the system does not permit the existence of compactly supported solutions that exhibit a moving front or interface, which has important implications for the simulation of more complex models that also feature this degenerate diffusive mechanism.
Source: The ANZIAM Journal
Author: MICHAEL DALLASTON
Institution: Queensland University of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W7164934035