Persistence versus extinction under a climate change in mixed environments
By Hoang-Hung Vo. 2014
59 citations recorded by the source corpus.
This paper is devoted to the study of the persistence versus extinction of species in the reaction-diffusion equation: \begin{equation} u_t-\Delta u=f(t,x_1-ct,y,u) \quad\quad t>0,\ x\in\Omega,\nonumber \end{equation} where $\Omega$ is of cylindrical type or partially periodic domain, $f$ is of Fisher-KPP type and the scalar $c>0$ is a given forced speed. This type of equation originally comes from a model in population dynamics (see \cite{BDNZ},\cite{PL},\cite{SK}) to study the impact of climate change on the persistence versus extinction of species. From these works, we know that the dynamics is governed by the traveling fronts $u(t,x_1,y)=U(x_1-ct,y)$, thus characterizing the set of traveling fronts plays a major role. In this paper, we first consider a more general model than the model of \cite{BDNZ} in higher dimensional space, where the environment is only assumed to be globally unfavorable with favorable pockets extending to infinity. We consider in two frameworks: the reaction term is time-independent or time-periodic dependent. For the latter, we study the concentration of the species when the environment outside $\Omega$ becomes extremely unfavorable and further prove a symmetry breaking property of the fronts.
Subfields: Applied Mathematics, Modeling and Simulation, Public Health, Environmental and Occupational Health
View Paper: https://www.semanticscholar.org/paper/8cb41ae452c8ae8d86fe10d0c1cb436608c6021b
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Citations in the corpus
- Spreading and Vanishing for a Monostable Reaction–Diffusion Equation with Forced Speed (2018, background): “This result also highlights qualitative differences with the KPP framework of [5, 6, 7, 17, 29], where the persistence of the population depends only on the value of c.”
- Persistence of species in a predator-prey system with climate change and either nonlocal or local dispersal (2021, background): “Moreover, propagation of the species in an unbounded favorable zone has been addressed in [27], and in time-periodic shifting habitat in [18, 30].”
- Spatial-temporal dynamics of a Lotka-Volterra competition model with nonlocal dispersal under shifting environment (2019, result): “Vo [35] removed the condition that the favorable zone has compact support in [6,7] and obtained similar results.”