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we study the nonnegative solutions of the viscous Hamilton-Jacobi problem \\[ \\left\\{\\begin{array} [c]{c}% u_{t}-\\nu\\Delta u+|\\nabla u|^{q}=0, u(0)=u_{0}, \\end{array} \\right. \\] in $Q_{\\Omega,T}=\\Omega\\times\\left(0,T\\right) ,$ where $q>1,\\nu\\geqq 0,T\\in\\left(0,\\infty\\right] ,$ and $\\Omega=\\mathbb{R}^{N}$ or $\\Omega$ is a smooth bounded domain, and $u_{0}\\in L^{r}(\\Omega),r\\geqq1,$ or $u_{0}% \\in\\mathcal{M}_{b}(\\Omega).$ We show $L^{\\infty}$ decay estimates, valid for \\textit{any weak solution}, \\textit{without any conditions a}s $\\left\\| x\\right\\| \\rightarrow\\infty,$ and \\textit{without un","authors_text":"Marie-Fran\\c{c}oise Bidaut-V\\'eron (LMPT), Nguyen Anh Dao (LMPT)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-02-13T09:46:03Z","title":"$L^{\\infty}$ estimates and uniqueness results for nonlinear parabolic equations with gradient absorption 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