Isolated initial singularities for the viscous Hamilton-Jacobi equation

Details Isolated initial singularities for the viscous Hamilton-Jacobi equation Isolated initial singularities for the viscous Hamilton-Jacobi equation

2012-01-09

arxiv.org/abs/1201.1774v1

Mathematics

Analysis of PDEs

32 pages

Scientific paper

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

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