8 problems

Schonbek's sharp decay-rate conjecture. The sharp decay rate of the velocity in $L^2$ should be

Let $(T(t))_{t\geq 0}$ be a bounded semigroup on a Hilbert space $X$ with infinitesimal generator $-A$ such that $\sigma(A)\cap i\mathbb{R}=\emptyset$. Define … and let…

For the perturbation variables $(\phi,\varphi,\zeta):=(\rho-\bar{\rho},u-\bar{u},\theta-\bar{\theta})$ of the planar entropy wave, the presence of a diffusion wave is expected to d…

Polynomial decay conjecture. The decay rate

Logarithmic-factor conjecture. The logarithmic factors in both estimates can be dropped for all values of $p$, so that

Consider the $N$-dimensional half-space analogue of the wave problem with damping coefficient $V(x)$ whose decay at spatial infinity is governed by a parameter $V_0$, and let…

Consider the one-dimensional half-line wave problem with damping coefficient $V(x)$ satisfying … and, for some $V_0>0$, $V_1\geq V_0$, and $L_2>0$, … Let $E(t)$ denote the energy o…

Let $B$ be a magnetic field, and let $\beta$ and $\tilde{u}$ be the parameters and rescaled heat evolution appearing in Theorem; denote by $\gamma_B$ the decay exponent in that the…