12 problems

Modified reproduction-number conjecture. The modified reproduction number is

Advection-induced asymmetry conjecture. The infection spreads not only due to diffusion but also due to advection, leading to asymmetric spatial distributions. The imaginary part o…

Exact spreading-speed conjecture. The free boundary $h(t)$ satisfies

Consider the epidemic models labeled (1.3)–(1.7), ordered according to the number of nonlocal reaction terms they contain. Nonlocal-reaction spreading difficulty conjecture. The mo…

Consider an age-structured model with nonlocal diffusion and its corresponding model with Laplace diffusion, and denote their principal eigenvalues by the associated spectral quant…

Preferential concentration conjecture. As $\alpha$ increases, the population should concentrate at positions $x$ where $m(x)$ is small.

Euclidean and geodesic distance propagation conjecture. There exists such an obstacle $K$ and datum $(J,f)$ for which the limiting solution $u_\infty$ satisfies

Spatially averaged logistic limit conjecture. We conjecture that $u_{\sigma}(x,t)$ can approximate the solution $v$ of this equation as the dispersal spread becomes small,…

Let $M^{D}_{\sigma,m,\Omega}+a$ be the nonlocal diffusion operator with Dirichlet boundary condition, where $m>2$, and let $\lambda_p(M^{D}_{\sigma,m,\Omega}+a)$ denote its general…

Let $P$ be the profile associated with a stable process, and let the property in question be the validity of conditions … with $\beta=\sigma$ for the corresponding operator. Stable…

Improved regularity conjecture. The regularity results for the regional fractional Laplacian might be improved to $u\trap C^{1,alpha/2}(\overline{Omega})$, at least in the one-dime…

Let $u$ be the solution of the fractional Laplacian equation on a bounded domain, let $\widetilde u_{N,\lambda}$ denote the corresponding nonlocal finite element solution, and let…