3 problems

Assume $(B,T)$, $(u_{0},u_{1})$, $d$, and $\Omega$ are given, and let $u$ be the unique maximal solution to the hyperbolic problem. Critical-threshold conjecture. There exist criti…

De Giorgi's conjecture. There exists a limit

For the scalar semilinear equation, let $n$ denote the spatial dimension, $m$ the physical mass, and let the nonlinearity exponent satisfy $\alpha\in(0,\infty)$. Forbidden physical…