3 problems

Let $\Omega_{\lambda}$ be the domain and let $\mathfrak{S}:=\{\lambda>0:\det(\mathcal{I}-\mathcal{R}_{\lambda})=0\}$, where $\mathcal{I}$ and $\mathcal{R}_{\lambda}$ are the operat…

Let the PD-WG finite element scheme use stabilization parameter $b3=0$, with polynomial indices $k$ and $s$, diffusion tensor $a$, convection vector ${\mathbf{b}}$, and meshsize su…

Let $u_0$ be initial data such that $H(u_0)\belongs to L^1(\Omega)$, and let $u$ be a weak solution in the sense of Definition. Renormalization conjecture. The weak solution $u$ is…