{"paper":{"title":"Spectral problems for non elliptic symmetric systems with dissipative boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.FA","authors_text":"Ferruccio Colombini, Jeffrey Rauch, Vesselin Petkov","submitted_at":"2013-03-15T11:43:24Z","abstract_excerpt":"This paper considers and extends spectral and scattering theory to dissipative symmetric systems that may have zero speeds and in particular to strictly dissipative boundary conditions for Maxwell's equations. Consider symmetric systems $\\partial_t - \\sum_{j=1}^n A_j \\partial_{x_j}$ in ${\\mathbb R}^n,\\: n \\geq 3$, $n$ odd, in a smooth connected exterior domain $\\Omega := {\\mathbb R}^n \\setminus \\bar{K}$. Assume that the rank of $A(\\xi) = \\sum_{j= 1}^n A_j \\xi_j$ is constant for $\\xi \\not= 0.$ For maximally dissipative boundary conditions on $\\Omega :={\\mathbb R}^n \\setminus \\bar{K}$ with bound"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3743","kind":"arxiv","version":3},"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"}