{"paper":{"title":"On a diffuse interface model of tumor growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Elisabetta Rocca, Maurizio Grasselli, Sergio Frigeri","submitted_at":"2014-05-14T10:45:58Z","abstract_excerpt":"We consider a diffuse interface model of tumor growth proposed by A.~Hawkins-Daruud et al. This model consists of the Cahn-Hilliard equation for the tumor cell fraction $\\varphi$ nonlinearly coupled with a reaction-diffusion equation for $\\psi$, which represents the nutrient-rich extracellular water volume fraction. The coupling is expressed through a suitable proliferation function $p(\\varphi)$ multiplied by the differences of the chemical potentials for $\\varphi$ and $\\psi$. The system is equipped with no-flux boundary conditions which entails the conservation of the total mass, that is, the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3446","kind":"arxiv","version":2},"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"}