5 problems

Let $X_0,X_1,\ldots,X_r$ be vector fields on a manifold, and consider an operator … Let the minimal time for mixing mean the least time at which the associated kernel $P_t$ has uni…

Uniqueness conjecture for sharp traveling waves. The sharp type traveling wave is unique, and the corresponding wave speed satisfies

For a stationary diffusion-degenerate front in the cases $\textbf{[sN}$mathbb{gtrless}$\textbf{]}$, let $\mathcal{L}$ denote the associated linearized operator and let…

Consider traveling fronts for systems of reaction–diffusion equations whose diffusion is represented by a degenerate diffusion tensor. Systems conjecture. The ideas introduced to h…

The paper studies spectral stability for smooth traveling fronts of reaction–diffusion equations with degenerate diffusion coefficients and speed $c>c_*$. Applicability conjecture.…