9 problems

Consider the semilinear regular Euler–Poisson–Darboux–Tricomi equation … bigl((m+1)n-1+mubigr)p^2-bigl((m+1)(n-2)+3+mubigr)p-2(m+1)=0. … . This conjecture proposes which of the Str…

Consider the initial value problem … with … where $p,q\in(1,\infty)\cup\{0\}$, $T>0$, $f$ and $g$ are smooth and compactly supported, and $\varepsilon>0$ is sufficiently small. Let…

Sharp lifespan conjecture. The sharp lifespan estimates above should still hold for every spatial dimension $n\geqslant 1$.

Transition-set optimality conjecture. The estimates in the two preceding theorems should be optimal except on these transition sets. In the critical case, the lifespan should satis…

Transition-curve optimality conjecture. The lifespan estimates in Theorem should be optimal except on this transition curve. On the curve,

Transition-surface logarithmic-gain conjecture. Lifespan estimates on the transition surfaces should admit a logarithmic improvement.

Let $(u_0,u_1)$ be nontrivial, nonnegative, compactly supported smooth initial data for the semilinear wave equation on an asymptotically Euclidean manifold, with small-data size ……

Takamura's conjecture. The lifespan satisfies

For the semilinear wave equation in dimension $n=2$ with quadratic nonlinearity, let $alpha=2$ and let $H$ denote the nonlinear term. The lifespan is denoted by…