{"paper":{"title":"A Finite Difference Method for Two-Phase Parabolic Obstacle-like Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Avetik Arakelyan","submitted_at":"2011-11-27T19:12:37Z","abstract_excerpt":"In this paper we treat the numerical approximation of the two-phase parabolic obstacle-like problem: \\[\\Delta u -u_t=\\lambda^+\\cdot\\chi_{\\{u>0\\}}-\\lambda^-\\cdot\\chi_{\\{u<0\\}},\\quad (t,x)\\in (0,T)\\times\\Omega,\\] where $T < \\infty, \\lambda^+ ,\\lambda^- > 0$ are Lipschitz continuous functions, and $\\Omega\\subset\\mathbb{R}^n$ is a bounded domain. We introduce a certain variational form, which allows us to define a notion of viscosity solution. We use defined viscosity solutions framework to apply Barles-Souganidis theory. The numerical projected Gauss-Seidel method is constructed. Although the pap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6287","kind":"arxiv","version":5},"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"}