B. Torebek

Sharp lifespan estimates for heat equations with H\"ormander operators

In this paper, we study the Cauchy problem $u_t-\mathcal L u=h(t)u^p$, $u(0)=\varepsilon u_0\ge0$, where $p>1$, $h\ge0$ is only locally integrable, and $\mathcal L=\sum_{j=1}^mX_j^2$ is a homogeneous H\"ormander sum of squares on $\mathbb R^n$ of homogeneous dimension $q$. Diffusion spreads the solution out and weakens...