5 problems

In the predator-prey system, let $c_e$ denote the habitat shift speed and let the predators' initial decay condition be as specified in the preceding spreading-speed analysis. Assu…

Let $u$ be the solution of the Cauchy problem associated with equation (1.1), and let $c_*$ be the spreading speed and $c_1$ the shifting speed. Convergence conjecture. If … then…

Let $m\in L^\infty(\mathbb{R})$ satisfy $\inf m>0$, and consider a Fisher–KPP equation whose linearization at $u=0$ has intrinsic growth rate $m(x-c_A t)$. Suppose that $m$ equals…

Let $c_1 \in (2\sqrt{r_2},2\sqrt{r_1}]$ be the speed of the shifting environment, and let $c^*$ denote the spreading speed of the predator population. In the case not covered by th…

Maximal-spreading-speed conjecture. In general, the presence of the chemo-attractant does not increase the maximal spreading speed.