10 problems

Let \boldsymbol{p}_{\eta}_{\eta>0} and c_{\eta}_{\eta\geq0} satisfy … Assume $(H_{7})$. Stability is understood as local asymptotic stability with respect to $(E_{KPP}^{0})$. Limit…

Let $\overline{\phi}\in \overline{K}(\mathbb{R})$ be an admissible kernel perturbation supported in $[-1/2,1/2]$, with $||\overline{\phi}||_1^m$ small. Consider parameters…

Let $u(x,t)$ solve the Neumann problem … with … and initial data $u(x,0)=u_0(x)$, where $u_0(x)>0$ for some $x$. Long-time convergence conjecture. … The claim describes the predict…

Consider the one-dimensional Dirichlet problem … with the Dirichlet boundary conditions and initial data specified in the paper, and let $u$ denote its solution. Large-population w…

Bounded front-width conjecture. For $b7<1$, almost surely,

Refined Fisher–KPP expansion conjecture. One has

Level-difference conjecture. One has

Fast-diffusion exponential propagation conjecture. For every $\sigma<\sigma_{\ast}$,

Full decay-characterization conjecture. For any solution $0<u<1$, the limit $\lambda$ exists in $[0,\sqrt{f'(0)}]$, and $u$ is a transition front connecting $0$ and $1$ if and only…

Asymptotic-speed and profile conjecture. Any such transition front has asymptotic past and future speeds $c_\pm$ satisfying