{"paper":{"title":"Global stability of solutions to nonlinear wave equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Shiwu Yang","submitted_at":"2012-05-18T19:00:45Z","abstract_excerpt":"We consider the problem of global stability of solutions to a class of semilinear wave equations with null condition in Minkowski space. We give sufficient conditions on the given solution which guarantees stability. Our stability result can be reduced to a small data global existence result for a class of semilinear wave equations with linear terms $B^{\\mu\\nu}\\patial_{\\mu}\\Phi(t, x)\\patial_{\\nu}\\phi$, $L^\\mu(t,x)\\patial_{\\mu}\\phi$ and quadratic terms $h^{\\mu\\nu}(t, x)\\patial_{\\mu}\\phi\\patial_{\\nu}\\phi$ where the functions $\\Phi(t, x)$, $L^\\mu(t, x)$, $h^{\\mu\\nu}(t, x)$ decay rather weakly and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4216","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"}