@misc{10498/39073,
year = {2026},
url = {http://hdl.handle.net/10498/39073},
abstract = {The survival of a population confined within a bounded habitat is a classical problem, traditionally analyzed in terms of the habitat size. In the linear case, persistence is ensured when the domain length exceeds a critical size lc. In nonlinear models, however survival conditions become considerably more complex and may even take less intuitive forms, such as l≤lc. In this context, Colombo and Anteneodo (2018) studied the power-law reaction–diffusion model ut=D(uν−1ux)x+auμ, with μ,ν>0, accompanied by hostile boundary conditions, determining survival thresholds in terms of habitat size for initially homogeneous populations. In this paper, we propose a general formulation of the persistence question by rewriting the power-law reaction–diffusion model in terms of suitable nondimensional variables. This approach reveals that persistence can be naturally expressed through a parameter [Formula Presented]. We show that there exists a critical value Qc depending on μ, ν and the initial distribution, such that survival occurs whenever Q≥Qc. This more intuitive condition reconciles the various survival criteria within a unified framework. To further explore this condition, we analyze two one-parameter families of initial distributions, including the homogeneous case, and apply a finite-difference scheme to estimate Qc. Conversely, for given model parameters μ, ν, l, n0, and the growth and diffusion coefficients a and D (and consequently the value of Q) we use the numerical algorithm to determine how concentrated the initial distribution must be to ensure population survival.},
publisher = {Elsevier},
keywords = {Population dynamics},
keywords = {Critical parameter},
keywords = {Initial distributions},
keywords = {Boundary conditions},
keywords = {Numerical analysis},
title = {A general formulation of the survival problem in a power-law reaction–diffusion model: Emergence of a critical parameter},
doi = {10.1016/J.PHYSD.2025.135037},
author = {Rosa Silva, Rafael de la and Medina Reus, Elena Blanca},
}