{"paper":{"title":"A nonlinear inequality and evolution problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"A.G.Ramm","submitted_at":"2010-09-30T13:58:36Z","abstract_excerpt":"Assume that $g(t)\\geq 0$, and $$\\dot{g}(t)\\leq -\\gamma(t)g(t)+\\alpha(t,g(t))+\\beta(t),\\ t\\geq 0;\\quad g(0)=g_0;\\quad \\dot{g}:=\\frac{dg}{dt}, $$ on any interval $[0,T)$ on which $g$ exists and has bounded derivative from the right, $\\dot{g}(t):=\\lim_{s\\to +0}\\frac{g(t+s)-g(t)}{s}$. It is assumed that $\\gamma(t)$, and $\\beta(t)$ are nonnegative continuous functions of $t$ defined on $\\R_+:=[0,\\infty)$, the function $\\alpha(t,g)$ is defined for all $t\\in \\R_+$, locally Lipschitz with respect to $g$ uniformly with respect to $t$ on any compact subsets$[0,T]$, $T<\\infty$, and non-decreasing with re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.6138","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"}