8 problems

Integrability-relaxation conjecture. The integrability assumptions in the definition of a weak solution could potentially be relaxed. The paper reports convergence of the diffusion…

Roos and Zarin's extension conjecture. The analysis of uniform supercloseness for the nonsymmetric discontinuous Galerkin method with interior penalties can be extended from proble…

Let $cvarphi^{\rm loc}$ be the local function on the patch $comega$, let $cgamma_{\partial_n}$ denote the normal-derivative trace on $cpartial\omega$, and let $cell$ be the localiz…

Multidimensional convergence conjecture. There exists a constant $C=C(R,k,m,|u|_{H^{m+2}(R_0)})$ such that

Let $u$ satisfy the convection-diffusion equation in Eq. (32), let $u_N$ be defined by Eq. (7), and suppose that, at the interpolation points $x_j$, … for $j=1,\ldots,N$, under the…

Let $M\ne0$, $\varepsilon\in(0,1)$, and consider the transport-diffusion equation on $(0,T)\times(0,L)$, … with boundary control at $x=0$, homogeneous boundary condition at $x=L$,…

Let $L$ be the operator on $L^2[-\pi,\pi]$ defined by … with periodic boundary conditions $y(-\pi)=y(\pi)$ and parameter $\epsilon>0$. Pure-imaginary spectrum conjecture. All eigen…

Let $u_M(x,t)$ be the unique nonnegative self-similar solution of … with initial data $u(x,0)=M\delta_0$, where $\alpha\in(1,2)$, $M>0$, and $b\in\mathbb{R}^d$ is fixed. Let…