{"paper":{"title":"Homotopy regularization for a high-order parabolic equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alejandro Ortega, Pablo \\'Alvarez-Caudevilla","submitted_at":"2019-03-22T15:19:28Z","abstract_excerpt":"In this work we study the solvability of the Cauchy Problem for a quasilinear degenerate high-order parabolic equation \\begin{equation*}\n  \\left\\{\n  \\begin{tabular}{lcl}\n  $u_t=(-1)^{m-1}\\nabla\\cdot(f^n(|u|)\\nabla\\Delta^{m-1}u)$ & &in $\\mathbb{R}^N\\times\\mathbb{R}_+$,\n  $u(x,0)=u_0(x)$& & in $\\mathbb{R}^N$,\n  \\end{tabular}\n  \\right. \\end{equation*} with $m\\in\\mathbb{N},\\ m>1$ and $n>0$ a fixed exponent. Moreover, $f$ is a continuous monotone increasing positive bounded function with $f(0)=0$ and the initial data $u_0(x)$ is bounded smooth and compactly supported. Thus, through an homotopy argu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.09552","kind":"arxiv","version":1},"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"}