Cantrell-Cosner-Lou concentration conjecture for positive local maxima

Let $u$ be the unique positive steady-state of the ecological model under (H1), where $m(x)\in C^{3}(\overline{\Omega})$ and is positive somewhere. The parameter $\alpha$ denotes the large advection parameter.

Cantrell-Cosner-Lou concentration conjecture. $u$ concentrates precisely on the set of positive local maximum points of $m(x)$ as $\alpha\rightarrow\infty$.

This conjecture concerns the concentration profile of the steady-state population as advection becomes large, refining known results that the total population tends to zero when the critical-point set of $m$ has Lebesgue measure zero and that, in one dimension under suitable finiteness assumptions, $u$ tends uniformly to zero away from critical points. The supplied text gives no resolution status for the conjecture.