{"paper":{"title":"$L^{\\infty}$ estimates and uniqueness results for nonlinear parabolic equations with gradient absorption terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Marie-Fran\\c{c}oise Bidaut-V\\'eron (LMPT), Nguyen Anh Dao (LMPT)","submitted_at":"2012-02-13T09:46:03Z","abstract_excerpt":"Here 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2674","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}