{"paper":{"title":"On the Cauchy problem for the reaction-diffusion system with point-interaction in $\\mathbb R^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Daniele Barbera, Mario Rastrelli, Vladimir Georgiev","submitted_at":"2025-04-11T11:46:59Z","abstract_excerpt":"The paper studies the existence of solutions for the reaction-diffusion equation in $\\mathbb R^2$ with point-interaction laplacian $\\Delta_\\alpha$ with $\\alpha\\in(-\\infty,+\\infty]$, assuming the functions to remain on the absolute continuous projection space. By semigroup estimates, we get the existence and uniqueness of solutions on $$ L^\\infty\\left((0,T);H^1_\\alpha\\left(\\mathbb R^2\\right)\\right)\\cap L^r\\left((0,T);H^{s+1}_\\alpha\\left(\\mathbb R^2\\right)\\right), $$ with $r>2$, $s<\\frac{2}{r}$ for the Cauchy problem with small $T>0$ or small initial conditions on $H^1_\\alpha(\\mathbb R^2)$. Fina"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.08460","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/2504.08460/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"}