3 problems

Let $L>0$, $M\in\mathbb{R}\setminus\{0\}$, and $\varepsilon>0$. Consider the transport–diffusion equation $u_t+M u_x=\varepsilon u_{xx}$ on $(0,T)\times(0,L)$, with a Dirichlet bou…

Let $n$ be a positive integer, let $\{I,H\}^n$ denote the transform set consisting of $n$ choices between the identity transform $I$ and the Hadamard transform $H$, and let the cli…

Let $\deg>0$, $j>0$, and $z>0$. Let $\hat{f}_{z,j}$ be the symbol appearing in the paper, and let $\lambda”_{\rm \min}(\hat{f}_{z,j})|_{0}$ denote the second derivative at $0$ of it…