{"paper":{"title":"Long Time Boundedness of Planar Jump Discontinuities for Homogeneous Hyperbolic Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jeffrey Rauch","submitted_at":"2019-01-13T15:12:06Z","abstract_excerpt":"Suppose that $L(\\partial_t,\\partial_x)$ is a homogeneous constant coefficient strongly hyperbolic partial differential operator on ${\\mathbb R}^{1+d}$ and $H$ is a characteristic hyperplane. Suppose that in a conic neighborhood of the conormal variety of $H$, the characteristic variety of $L$ is the graph of a real analytic function $\\tau(\\xi)$ with ${\\rm rank}\\,\\tau_{\\xi\\xi}$ identically equal to zero or the maximal possible value $d-1$. Suppose that the source function $f$ is compactly supported in $t\\ge 0$ and piecewise smooth with singularities only on $H$. Then the solution of $Lu=f$ with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.03997","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"}