Isolated initial singularities for the viscous Hamilton-Jacobi equation

Here we study the nonnegative solutions of the viscous Hamilton-Jacobi equation [u_{t}-\Delta u+|\nabla u|^{q}=0] in $Q_{\mathrm{\Omega },T}=\mathrm{\Omega }\times (0,T),$ where $q>1,T\in (0,\mathrm{\infty }],$ and $\mathrm{\Omega }$ is a smooth bounded domain of $\mathbb{R}$ containing $0,$ or $\mathrm{\Omega }={\mathbb{R}}^N\mathrm{.}$ We consider solutions with a possible singularity at point $(x,t)=(0,0)\mathrm{.}$ We show that if $q\ge q_{\ast }=(N+2)\mathrm{/}(N+1)$ the singularity is removable.