3 problems

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…

Convergence conjecture. For $(a,D)\in\mathcal{H}_1$, the solution to (DIVP) approaches the temporally stable unique $r$-peak steady state as $t\to\infty$ uniformly for $x\in[0,a]$.

Let $u$ be the solution considered in Theorem, and let $\Omega(u)$ denote its omega-limit set. Write $\mathcal{E}$ for the set defined in the paper, and let $\varphi$ be the minima…