{"paper":{"title":"Boundedness and evolution rates for a quasilinear reaction-diffusion equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ariel S\\'anchez, Marta Latorre, Razvan Gabriel Iagar","submitted_at":"2026-06-07T22:27:03Z","abstract_excerpt":"We consider the following quasilinear reaction-diffusion equation $$ \\partial_tu=\\Delta u^m+(1+|x|)^{\\sigma}u^p, \\quad (x,t)\\in\\mathbb{R}^N\\times(0,\\infty), $$ in dimension $N\\geq3$ and in the range of exponents $1<p<m$ and $-\\infty<\\sigma<-2$. We prove that, for initial conditions $u_0$ satisfying $$ u_0\\geq0, \\quad u_0\\not\\equiv0, \\quad \\lim\\limits_{|x|\\to\\infty}|x|^{-(\\sigma+2)/(m-p)}u_0(x)=0, $$ the solution $u$ to the corresponding Cauchy problem remains uniformly bounded from above and below: $$ C_1\\leq \\|u(t)\\|_{\\infty}\\leq C_2, \\quad t\\in(0,\\infty), $$ for some positive constants $C_1$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08861","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.08861/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}