7 problems

Let $u(x,t)$ be the transition front solution constructed in the paper for the nonlocal dispersal equation in the exterior domain. A global mean speed conjecture asserts that there…

Stability and attraction conjecture. These solutions are stable with respect to small perturbations and attract all solutions of the Cauchy problem whose initial data are asymptoti…

Complete-propagation counterexample conjecture. In general, there may exist transition fronts with complete propagation and without global mean speed.

Converse mean-speed conjecture. The complete propagation of all the front-like solutions $u_i$ is equivalent to the property that all transition fronts connecting $0$ and $1$ have…

For a measure $\mu$ as in Theorem, suppose that there is $\zeta\in S^{d-1}$ such that $\operatorname{supp}(\mu)\subseteq \mathcal{W}_{0,\zeta}$, but $\operatorname{supp}(\mu)$ is n…

Attractivity conjecture. In this case, the critical travelling wave is attractive for Heaviside-type initial data.

Let $u$ be the solution of the Cauchy problem considered in Theorem … xa(t)-xb(t)to+inftyquadtext{as }tto+infty. … , $x_a(t)-x_b(t)\to+\infty$ as $t\to+\infty$ for any $0<a<b<1$. T…