{"paper":{"title":"Dynamics of Time-Periodic Reaction-Diffusion Equations with Compact Initial Support on R","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hiroshi Matano, Weiwei Ding","submitted_at":"2018-07-11T14:06:40Z","abstract_excerpt":"This paper is concerned with the asymptotic behavior of bounded solutions of the Cauchy problem \\begin{equation*} \\left\\{ \\begin{array}{ll} u_t=u_{xx} +f(t,u), & x\\in\\mathbb{R},\\,t>0,\\\\ u(x,0)= u_0, & x\\in\\mathbb{R}, \\end{array}\\right. \\end{equation*} where $u_0$ is a nonnegative bounded function with compact support and $f$ is a rather general nonlinearity that is periodic in $t$ and satisfies $f(\\cdot,0)=0$. In the autonomous case where $f=f(u)$, the convergence of every bounded solution to an equilibrium has been established by Du and Matano (2010). However, the presence of periodic forcing"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04146","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"}