5 problems

Let the semi-implicit scheme for the Cahn–Hilliard equation produce solutions with energy defined by the paper's equation (energy0). Energy stability conjecture. The energy stabili…

Let $varepsilon>0$ denote the interfacial thickness parameter, and consider the stochastic Cahn–Hilliard equation with a non-vanishing noise term, meaning $gamma=0$. Let the stocha…

Let $\alpha$ and $\beta$ be parameters in the Ginzburg–Landau equation. For $\alpha=\beta\neq 0$, consider the Cahn–Hilliard equation … with real-valued coefficients $\nu_2$,…

Critical energy-barrier conjecture. In the critical regime, the energy barrier is, to leading order,

Let $u$ be a weak solution of the nonlocal elliptic equation on $\Omega$, with the nonlocal operator $\mathcal{L}$ and the associated bilinear form as in the paper. The preceding a…