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arXiv · 1201.1774

Isolated initial singularities for the viscous Hamilton-Jacobi equation

Marie-Françoise Bidaut-Véron·Nguyen Anh Dao
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Abstract

Here we study the nonnegative solutions of the viscous Hamilton-Jacobi equation [u_{t}-Δu+|\nabla u|^{q}=0] in $Q_{Ω,T}=Ω\times(0,T),$ where $q>1,T\in(0,\infty] ,$ and $Ω$ is a smooth bounded domain of $\mathbb{R}% ^{N}$ containing $0,$ or $Ω=\mathbb{R}^{N}.$ 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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Marie-Françoise Bidaut-Véron, Nguyen Anh Dao. 2012-01-09. Isolated initial singularities for the viscous Hamilton-Jacobi equation. https://arxiv.org/abs/1201.1774

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