{"paper":{"title":"Recovering the initial condition and physical coefficients in a nonlinear PDE model of cell invasion","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.AP","authors_text":"Beiji Chen, Kui Ren","submitted_at":"2026-06-10T01:24:52Z","abstract_excerpt":"This paper investigates an inverse problem for the simultaneous reconstruction of two spatially varying reaction coefficients, the local proliferation rate and the competition (saturation) coefficient, together with the unknown initial condition, in a nonlinear, density-dependent reaction-diffusion model motivated by cell invasion and tumor growth dynamics. Using Carleman estimates, we establish a global uniqueness result together with a Lipschitz-type stability estimate for the reaction coefficients and a weaker, logarithmic stability estimate for the initial condition. For the numerical reco"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11554","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/2606.11554/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"}