{"paper":{"title":"Cauchy problem for effectively hyperbolic operators with triple characteristics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tatsuo Nishitani, Vesselin Petkov","submitted_at":"2017-06-19T14:11:20Z","abstract_excerpt":"We study the Cauchy problem for effectively hyperbolic operators $P$ with principal symbol $p(t, x,\\tau,\\xi)$ having triple characteristics on $t = 0$. Under a condition (E) we show that such operators are strongly hyperbolic, that is the Cauchy problem is well posed for $p(t, x,D_t, D_x) + Q(t, x, D_t, D_x)$ with arbitrary lower order term $Q$. The proof is based on energy estimates with weight $t^{-N}$ for a first order pseudo-differential system, where $N$ depends on lower order terms. For our analysis we construct a non-negative definite symmetrizer $S(t)$ and we prove a version of Fefferm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05965","kind":"arxiv","version":2},"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"}