Moving gradient singularity for the evolutionary $p$-Laplace equation
Erik Lindgren, Jin Takahashi · arXiv (Cornell University) · 2024
We consider the evolutionary $p$-Laplace equation in $\mathbb{R}^n$. For $p>n$, we construct a solution $u$ with a moving gradient singularity in the sense that $| abla u(x,t)|\to \infty$ for each $t$ as $x\toξ(t)$, where $ξ:[0,\infty)\to\mathbb{R}^n$ is a given curve.