{"paper":{"title":"Decay estimates for solutions of nonlocal semilinear equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luigi Rodino, Marco Cappiello, Todor Gramchev","submitted_at":"2012-03-09T13:28:52Z","abstract_excerpt":"We investigate the decay for $|x|\\rightarrow \\infty$ of weak Sobolev type solutions of semilinear nonlocal equations $Pu=F(u)$. We consider the case when $P=p(D)$ is an elliptic Fourier multiplier with polyhomogeneous symbol $p(\\xi)$ and derive sharp algebraic decay estimates in terms of weighted Sobolev norms. In particular, we state a precise relation between the singularity of the symbol at the origin and the rate of decay of the corresponding solutions. Our basic example is the celebrated Benjamin-Ono equation {equation} \\label{BO}(|D|+c)u=u^2, \\qquad c>0,{equation} for internal solitary w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2075","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"}