9 problems

Let $u_\mathrm{pl}(\xi,\tau)$ be a modulated pulled pattern-forming front satisfying the stated pinched-double-root, periodic-wake, exponential-asymptotic, marginal-Floquet-stabili…

Let $u_\mathrm{ps}(\xi,\tau)$ be a modulated pushed pattern-forming front, namely a temporally modulated pushed front leaving a pattern-forming wake. Selection of modulated pushed…

Let $u_\mathrm{pl}$ be a rigid pulled pattern-forming front, meaning a rigid front with marginal spectral stability that leaves behind a diffusively stable periodic pattern and has…

Let $u_\mathrm{tr}$ be a pushed-to-pulled transition front. A pushed-to-pulled transition front is a front at the boundary between pushed and pulled invasion, characterized here by…

Formal front-propagation conjecture. There exists an interval of trait values $J_0$ centered at $1$ such that, for every open interval $J\subset J_0$ centered at $1$, the density…

Let $K(\theta)$ be the directional spreading speed and define the Wulff shape by … Let $\hat{\mathscr{F}}$ be the convex hull of the Frank diagram, let…

Let $\theta$ be the direction of a zigzag front, and let $\theta_{\mathrm{m}}(t)$ and $\theta_{\mathrm{p}}(t)$ determine the two angles forming a peak, namely…

Let $u_\omega$ be the solution from Definition, under the hypotheses of Theorem (i) but without its limitation on the dimension $d$, and let $L_{u_\omega,\eta}(t)$ denote the trans…

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