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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1903.06331","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-15T02:43:42Z","cross_cats_sorted":[],"title_canon_sha256":"8e839e3c8b10b0f698a9ccc8dfcabb077c9bc0f4a30cc9189f0b31e423e9af8f","abstract_canon_sha256":"d3ccf9c9ab17c7761bbfefcf0485189dc3206ecf06457c1389920a63264df6b9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:11.097206Z","signature_b64":"9fQ+Bg3hqOchknfPGKWMBixO8w/ew/kPcGjCwsPEwW5e94DL4f0e7VPebkJ6jT626TzuIaf4fIKZ7Se5TFTQBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1394ba019e7e26b06b6ca81e77adbf76d0a32e957725815806971be63bdd722f","last_reissued_at":"2026-05-17T23:51:11.096829Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:11.096829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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} - 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