{"paper":{"title":"Multiple-interface solutions of one dimensional generalized parabolic Cahn-Hilliard equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chao Liu, Jun Yang","submitted_at":"2023-03-30T10:53:13Z","abstract_excerpt":"We consider one dimensional generalized parabolic Cahn-Hilliard equation $$ u_t=-\\partial_{xx}\\big[\\partial_{xx}u-W'(u)\\big]+W''(u)\\big[\\partial_{xx} u -W'(u)\\big], \\qquad \\forall\\, (t,x)\\in [0,+\\infty)\\times {\\mathbb R}, $$ where the function $W(\\cdot)$ is the standard double-well potential. For any given positive integer $k\\geq2$, we construct a solution $u(t,x)$ with $k$ interfaces, which has the form $$ u(t,x)\\approx\\sum_{j=1}^k(-1)^{j+1}\\omega\\big(x-\\gamma_j(t)\\big)-\\frac{1+(-1)^k}{2}\\qquad \\text{as}\\ t\\rightarrow +\\infty, $$ where $\\omega$ is the solution to the Allen-Cahn equation $$ \\o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.17288","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/2303.17288/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"}