{"paper":{"title":"Solutions with single radial interface of the generalized Cahn-Hilliard flow","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chao Liu, Jun Yang","submitted_at":"2022-09-29T02:52:37Z","abstract_excerpt":"We consider the generalized parabolic Cahn-Hilliard equation $$ u_t=-\\Delta\\left[\\Delta u -W'(u)\\right]+W''(u)\\left[\\Delta u -W'(u)\\right] \\qquad \\forall\\, (t, x)\\in \\widetilde{{\\mathbb R}}\\times{\\mathbb R}^n, $$ where $n=2$ or $n\\geq 4$, $W(\\cdot)$ is the typical double-well potential function and $\\widetilde{\\mathbb R}$ is given by $$ \\widetilde{\\mathbb R}=\\left\\{\n  \\begin{array}{rl}\n  (0, \\infty), &\\quad \\mbox{if } n=2,\n  (-\\infty, 0), & \\quad\\mbox{if } n\\geq 4.\n  \\end{array}\n  \\right. $$ We construct a radial solution $u(t, x)$ possessing an interface. At main order this solution consists "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.14522","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.14522/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}