{"paper":{"title":"A note for global existence of a two-dimensional chemotaxis-haptotaxis model with remodeling of non-diffusible attractant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiashan Zheng","submitted_at":"2017-11-27T23:37:27Z","abstract_excerpt":"In this paper, we study the following the coupled chemotaxis--haptotaxis model with remodeling of non-diffusible attractant\n$$\n\\left\\{\\begin{array}{ll} u_t = \\Delta u-\\chi\\nabla\\cdot(u\\nabla v)- \\xi\\nabla\\cdot(u\\nabla w)+\\mu u(1- u-w), \\displaystyle{v_t=\\Delta v- v +u},\\quad \\displaystyle{w_t=- vw+\\eta w(1-u-w)},\\quad \\end{array}\\right.\n$$\nin a bounded smooth domain $\\mathbb{R}^2$ with zero-flux boundary conditions, where $\\chi$, $\\xi$ and $\\eta$ are positive parameters. Under appropriate regularity assumptions on the initial data $(u_0, v_0, w_0)$, by develops some $L^p$-estimate techniques, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10044","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"}