{"paper":{"title":"Profile of touch-down solution to a nonlocal MEMS model","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giao Ky Duong, Hatem Zaag","submitted_at":"2018-11-28T10:18:06Z","abstract_excerpt":"In this paper, we are interested in the mathematical model of MEMS devices which is presented by the following equation on $(0,T) \\times \\Omega:$ \\begin{eqnarray*}\n  \\partial_t u = \\Delta u +\\displaystyle \\frac{\\lambda }{ (1-u)^2 \\left( 1 +\\displaystyle \\gamma \\int_{\\Omega} \\frac{1}{1-u} dx \\right)^2}, \\quad 0 \\leq u <1, \\end{eqnarray*} where $\\Omega$ is a bounded domain in $\\mathbb{R}^n$ and $\\lambda, \\gamma > 0$. In this work, we have succeeded to construct a solution which quenches in finite time T only at one interior point $a \\in \\Omega$. In particular, we give a description of the quench"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.11483","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"}