{"paper":{"title":"Nonclassic boundary value problems in the theory of irregular systems of equations with partial derivatives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Denis Sidorov, Nikolai Sidorov","submitted_at":"2016-10-09T13:14:10Z","abstract_excerpt":"The linear PDE ${\\mathbf B} {\\mathbf L} (\\frac{\\partial}{\\partial x}) u ={\\mathbf L}_1(\\frac{\\partial}{\\partial x})u +f(x)$ with nonclassic conditions on boundary $\\partial \\Omega$ is considered. Here ${\\mathbf B}$ is linear noninvertible bounded operator acting from linear space $E$ into $E,$ $x=(t,x_1,\\dots, x_m) \\in \\Omega, $ $\\Omega \\subset {\\mathbb R}^{m+1}.$ It is assumed that ${\\mathbf B}$ enjoys the skeleton decomposition ${\\mathbf B}={\\mathbf A}_1 {\\mathbf A}_2,$ ${\\mathbf A}_2 \\in {\\mathcal L}(E\\rightarrow E_1),$ ${\\mathbf A}_1 \\in {\\mathcal L}(E_1\\rightarrow E)$ where $E_1$ is linea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02673","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"}