Communications in Mathematical Sciences
Volume 14 (2016)
Effects of an advection term in nonlocal Lotka–Volterra equations
Pages: 1181 – 1188
Nonlocal Lotka–Volterra equations have the property that solutions concentrate as Dirac masses in the limit of small diffusion. In this paper, we show how the presence of an advection term changes the location of the concentration points in the limit of small diffusion and slow drift. The mathematical interest lies in the formalism of constrained Hamilton–Jacobi equations. Our motivations come from previous models of evolutionary dynamics in phenotype-structured populations [R.H. Chisholm, T. Lorenzi, A. Lorz, et al., Cancer Res., 75, 930–939, 2015], where the diffusion operator models the effects of heritable variations in gene expression, while the advection term models the effect of stress-induced adaptation.
nonlocal Lotka–Volterra equations, Dirac masses, phenotype-structured populations, stress-induced adaptation
2010 Mathematics Subject Classification
35R09, 45M05, 92D15, 92D25