This review describes reaction-advection-diffusion models for the ecological effects and
evolution of dispersal, and mathematical methods for analyzing those models. The topics …

… The coefficients bii represent intraspecies density dependence, in analogy with the term c(t)P
in (1.3), so we have bii ≤ 0 for all i. The coefficients bij, i = j, describe interactions between …

… on patches A, B, and C, the values for the principal eigenvalue … C, reflecting differences in
the amount of core habitat. In contrast, the perimeter‐to‐area ratio is large for patches B and C …

… The parameter C becomes relevant when encounters involve more than one predator
per prey in such a way that the predators share the killing and consumption of prey items, (This …

… is unstable for C small but globally asymptotically stable for C large, in particular if (3.6)
holds. Thus, when (3.3) holds, C plays an important role in determining the stability of u∗ v∗ . In …

Niemann-Pick type C (NPC) disease is predominantly caused by mutations in the NPC1
protein that affect intracellular cholesterol trafficking and cause accumulation of unesterified …

… We assume m(x) e L(Q) and that c is a positive constant. Let A denote the inverse of —A …
In that case, choose Eo to be any fixed measurable subset of Q with Eo c Eo and |£0 | mi ~ l^…

… We use C ij to denote the migration rate of humans from patches j to i and D ij to denote the
… , so that if C 21 is sufficiently large we have R 0 < 1 in (3.11). Recall that the parameter C 21 …

We study the existence, uniqueness, and stability of coexistence states in the Lotka–Volterra
model with diffusion for two competing species. We assume that the parameters describing …

… supplemented with boundary conditions on Of 2 x (0, ~) with d > 0 representing the rate
of diffusion, m(x) the intrinsic rate of population growth or decay at the point x, c(x) > 0 the …