RT journal article
T1 A general formulation of the survival problem in a power-law reaction–diffusion model: Emergence of a critical parameter
A1 Rosa Silva, Rafael de la
A1 Medina Reus, Elena Blanca
A2 Matemáticas
K1 Population dynamics
K1 Critical parameter
K1 Initial distributions
K1 Boundary conditions
K1 Numerical analysis
AB 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.
PB Elsevier
SN 0167-2789
YR 2026
FD 2026
LK http://hdl.handle.net/10498/39073
UL http://hdl.handle.net/10498/39073
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 09-may-2026