{"paper":{"title":"Smooth solutions and singularity formation for the inhomogeneous nonlinear wave equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Geng Chen, Robin Young","submitted_at":"2011-05-16T18:53:36Z","abstract_excerpt":"We study the nonlinear inhomogeneous wave equation in one space dimension: $v_{tt} - T(v,x)_{xx} = 0$. By constructing some \"decoupled\" Riccati type equations for smooth solutions, we provide a singularity formation result without restrictions on the total variation of unknown, which generalize earlier singularity results of Lax and the first author. These results are applied to several one-dimensional hyperbolic models, such as compressible Euler flows with a general pressure law, elasticity in an inhomogeneous medium, transverse MHD flow, and compressible flow in a variable area duct."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3174","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"}