{"paper":{"title":"A tumor growth model of Hele-Shaw type as a gradient flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"L\\'ena\\\"ic Chizat, Simone Di Marino","submitted_at":"2017-12-17T14:47:28Z","abstract_excerpt":"In this paper, we characterize a degenerate PDE as the gradient flow in the space of nonnegative measures endowed with an optimal transport-growth metric. The PDE of concern, of Hele-Shaw type, was introduced by Perthame et. al. as a mechanical model for tumor growth and the metric was introduced recently in several articles as the analogue of the Wasserstein metric for nonnegative measures. We show existence of solutions using minimizing movements and show uniqueness of solutions on convex domains by proving the Evolutional Variational Inequality. Our analysis does not require any regularity "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06124","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"}