{"paper":{"title":"Stable self-similar blow up for energy subcritical wave equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Birgit Sch\\\"orkhuber, Roland Donninger","submitted_at":"2012-01-20T16:48:54Z","abstract_excerpt":"We consider the semilinear wave equation \\[ \\partial_t^2 \\psi-\\Delta \\psi=|\\psi|^{p-1}\\psi \\] for $1<p\\leq 3$ with radial data in $\\R^{3}$. This equation admits an explicit spatially homogeneous blow up solution $\\psi^T$ given by $$ \\psi^T(t,x)=\\kappa_p (T-t)^{-\\frac{2}{p-1}} $$ where $T>0$ and $\\kappa_p$ is a $p$-dependent constant. We prove that the blow up described by $\\psi^T$ is stable against small perturbations in the energy topology. This complements previous results by Merle and Zaag. The method of proof is quite robust and can be applied to other self-similar blow up problems as well"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4337","kind":"arxiv","version":3},"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"}