2014/12/02 by Hoang‐Hung Vo, Vo, Hoang-Hung
Medicine · Biochemistry, Genetics and Molecular Biology · Mathematics · #Mathematical and Theoretical Epidemiology and Ecology Models #Evolution and Genetic Dynamics #Mathematical Biology Tumor Growth
paper · pdf · doi:10.48550/arxiv.1412.0907
This paper is devoted to the study of the persistence versus extinction of\nspecies in the reaction-diffusion equation: \ut-
Deltaν=f(t,x1-ct,y,u)
quad
quad tgt;0,
x
in
Omega,
nonumber where\n\Ω is of cylindrical type or partially periodic domain, f is of\nFisher-KPP type and the scalar c>0 is a given forced speed. This type of\nequation originally comes from a model in population dynamics (see\n citeBDNZ, citePL, citeSK) to study the impact of climate change on the\npersistence versus extinction of species. From these works, we know that the\ndynamics is governed by the traveling fronts u(t,x1,y)=U(x1-ct,y), thus\ncharacterizing the set of traveling fronts plays a major role. In this paper,\nwe first consider a more general model than the model of citeBDNZ in higher\ndimensional space, where the environment is only assumed to be globally\nunfavorable with favorable pockets extending to infinity. We consider in two\nframeworks: the reaction term is time-independent or time-periodic dependent.\nFor the latter, we study the concentration of the species when the environment\noutside \Ω becomes extremely unfavorable and further prove a symmetry\nbreaking property of the fronts.\n