{"paper":{"title":"Asymptotic behavior of solutions for linear parabolic equations with general measure data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francesco Petitta","submitted_at":"2014-09-19T09:18:48Z","abstract_excerpt":"In this paper we deal with the asymptotic behavior as $t$ tends to infinity of solutions for linear parabolic equations whose model is $$ \\begin{cases} u_{t}-\\Delta u = \\mu & \\text{in}\\ (0,T)\\times\\Omega,\\\\[0.7 ex] u(0,x)=u_0 & \\text{in}\\ \\Omega, \\end{cases} $$ where $\\mu$ is a general, possibly singular, Radon measure which does not depend on time, and $u_0\\in L^{1}(\\Omega)$. We prove that the duality solution, which exists and is unique, converges to the duality solution (as introduced by G. Stampacchia) of the associated elliptic problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5564","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"}