8 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…

Nonlinear stability conjecture. All $N$-spot ring patterns are nonlinearly stable unless the spot-spot distance is the smallest binding distance.

Consider the modified system … where the coupling term $\beta v$ has been replaced by $\beta\sigma(x)v$, and suppose that the Fourier transform of $\sigma(x)$ has full support. Res…

Let $S>0$ and consider the core problem eqref{eq:core}, whose ground state solution is denoted by $(U(\rho;S),V(\rho;S))$, with $mu(S)$ the associated eigenvalue function. A soluti…

Hexagon patch wavenumber-selection conjecture. Every stationary and invading stable hexagon 2D patch solution selects a unique hexagon cellular pattern. Its wavenumbers are determi…