{"paper":{"title":"Stability of planar traveling waves in a Keller-Segel equation on an infinite strip domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jihoon Lee, Kyudong Choi, Kyungkeun Kang, Myeongju Chae","submitted_at":"2016-09-03T12:00:48Z","abstract_excerpt":"A simplified model of the tumor angiogenesis can be described by a Keller-Segel equation \\cite{FrTe,Le,Pe}. The stability of traveling waves for the one dimensional system has recently been known by \\cite{JinLiWa,LiWa}. In this paper we consider the equation on the two dimensional domain $ (x, y) \\in\n  \\mathbf R \\times {\\mathbf S^{\\lambda}}$ for a small parameter $\\lambda>0$ where $ \\mathbf S^{\\lambda}$ is the circle of perimeter $\\lambda$. Then the equation allows a planar traveling wave solution of invading types. We establish the nonlinear stability of the traveling wave solution if the ini"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00821","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"}