{"paper":{"title":"Nonlinear parabolic problems in Musielak--Orlicz spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Agnieszka \\'Swierczewska-Gwiazda","submitted_at":"2013-06-10T12:45:39Z","abstract_excerpt":"Our studies are directed to the existence of weak solutions to a parabolic problem containing a multi-valued term. The problem is formulated in the language of maximal monotone graphs. We assume that the growth and coercivity conditions of a nonlinear term are prescribed by means of time and space dependent $N$--function. This results in formulation of the problem in generalized Musielak-Orlicz spaces. We are using density arguments, hence an important step of the proof is a uniform boundedness of appropriate convolution operators in Musielak-Orlicz spaces. For this purpose we shall need to as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2186","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"}