{"paper":{"title":"Liouville theorems for scaling invariant superlinear parabolic problems with gradient structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Pavol Quittner","submitted_at":"2014-09-17T12:01:38Z","abstract_excerpt":"We provide a simple method for obtaining new Liouville theorems for scaling invariant superlinear parabolic problems with gradient structure. To illustrate the method we prove Liouville theorems (guaranteeing nonexistence of positive classical solutions) for the following model problems: the scalar nonlinear heat equation $$ u_t-\\Delta u=u^p \\qquad\\hbox{in}\\ {\\mathbb R}^n\\times{\\mathbb R}, $$ its vector-valued generalization with a $p$-homogeneous nonlinearity and the linear heat equation in ${\\mathbb R}^n_+\\times{\\mathbb R}$ complemented by nonlinear boundary conditions of the form $\\partial "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4960","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"}