{"paper":{"title":"On the global existence and qualitative behavior of one-dimensional solutions to a model for urban crime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Michael Winkler, Nancy Rodriguez","submitted_at":"2019-03-15T02:43:42Z","abstract_excerpt":"We consider the no-flux initial-boundary value problem for the cross-diffusive evolution system \\begin{eqnarray*}\n  \\left\\{ \\begin{array}{ll}\n  u_t = u_{xx} - \\chi \\big(\\frac{u}{v} \\partial_x u \\big)_x - uv +B_1(x,t),\n  \\qquad & x\\in \\Omega, \\ t>0, \\\\[1mm]\n  v_t = v_{xx} +uv - v + B_2(x,t),\n  \\qquad & x\\in \\Omega, \\ t>0,\n  \\end{array} \\right. \\end{eqnarray*}\n  which was introduced by Short et al. in [Short2008] with $\\chi=2$ to describe the dynamics of urban crime\n  In bounded intervals $\\Omega\\subset\\mathbb{R}$ and with prescribed suitably regular nonnegative\n  functions $B_1$ and $B_2$, we f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.06331","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"}