{"paper":{"title":"Local and Global Dynamic Bifurcations of Nonlinear Evolution Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Desheng Li, Zhi-qiang Wang","submitted_at":"2016-12-24T03:31:41Z","abstract_excerpt":"We present new local and global dynamic bifurcation results for nonlinear evolution equations of the form $u_t+A u=f_\\lambda(u)$ on a Banach space $X$, where $A$ is a sectorial operator, and $\\lambda\\in R$ is the bifurcation parameter. Suppose the equation has a trivial solution branch $\\{(0,\\lambda):\\,\\,\\lambda\\in R\\}$. Denote $\\Phi_\\lambda$ the local semiflow generated by the initial value problem of the equation. It is shown that if the crossing number $n$ at a bifurcation value $\\lambda=\\lambda_0$ is nonzero and moreover, $S_0=\\{0\\}$ is an isolated invariant set of $\\Phi_{\\lambda_0}$, then"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08128","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"}