{"paper":{"title":"On the formation of shock for quasilinear wave equations by pulse with weak intensity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Shuang Miao","submitted_at":"2016-10-13T16:01:08Z","abstract_excerpt":"In this paper we continue to study the shock formation for the $3$-dimensional quasilinear wave equation \\begin{align}\\label{main eq} -(1+3G\"(0)(\\partial_{t}\\phi)^{2})\\partial^{2}_{t}\\phi+\\Delta\\phi=0,\\tag{\\textbf{$\\star$}} \\end{align} with $G\"(0)$ being a non-zero constant. Since \\eqref{main eq} admits global-in-time solution with small initial data, to present shock formation, we consider a class of large data. Moreover, no symmetric assumption is imposed on the data. Compared to our previous work [18], here we pose data on the hypersurface $\\{(t,x)|t=-r_{0}\\}$ instead of $\\{(t,x)|t=-2\\}$, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04147","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"}