{"paper":{"title":"Dissipative property for a class of non local evolution equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Antonio R. G. Garcia, Bruna E. P. Lucena, Severino H. da Silva","submitted_at":"2017-05-26T20:04:54Z","abstract_excerpt":"In this work we consider the non local evolution problem \\[ \\begin{cases} \\partial_t u(x,t)=-u(x,t)+g(\\beta K(f\\circ u)(x,t)+\\beta h), ~x \\in\\Omega, ~t\\in[0,\\infty[;\\\\ u(x,t)=0, ~x\\in\\mathbb{R}^N\\setminus\\Omega, ~t\\in[0,\\infty[;\\\\ u(x,0)=u_0(x),~x\\in\\mathbb{R}^N, \\end{cases} \\] where $\\Omega$ is a smooth bounded domain in $\\mathbb{R}^N, ~g,f: \\mathbb{R}\\to\\mathbb{R}$ satisfying certain growing condition and $K$ is an integral operator with symmetric kernel, $ Kv(x)=\\int_{\\mathbb{R}^{N}}J(x,y)v(y)dy.$ We prove that Cauchy problem above is well posed, the solutions are smooth with respect to ini"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09702","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"}