{"paper":{"title":"Time discretization of a nonlinear phase field system in general domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Pierluigi Colli, Shunsuke Kurima","submitted_at":"2018-11-26T22:57:00Z","abstract_excerpt":"This paper deals with the nonlinear phase field system\n  \\begin{equation*}\n  \\begin{cases}\n  \\partial_t (\\theta +\\ell \\varphi) - \\Delta\\theta = f\n  & \\mbox{in}\\ \\Omega\\times(0, T),\n  \\\\[1mm]\n  \\partial_t \\varphi - \\Delta\\varphi + \\xi + \\pi(\\varphi)\n  = \\ell \\theta,\\ \\xi\\in\\beta(\\varphi)\n  & \\mbox{in}\\ \\Omega\\times(0, T)\n  \\end{cases}\n  \\end{equation*} in a general domain $\\Omega\\subseteq\\mathbb{R}^N$. Here $N \\in \\mathbb{N}$, $T>0$, $\\ell>0$, $f$ is a source term, $\\beta$ is a maximal monotone graph and $\\pi$ is a Lipschitz continuous function. We note that in the above system the nonlinearity"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.10730","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"}