{"paper":{"title":"Convergence to equilibrium for positive solutions of some mutation-selection model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jerome Coville (BIOSP)","submitted_at":"2013-08-29T13:56:56Z","abstract_excerpt":"In this paper we are interested in the long time behaviour of the positive solutions of the mutation selection model with Neumann Boundary condition: $$ \\frac{\\partial u(x,t)}{dt}=u\\left[r(x)-\\int_{\\O}K(x,y)|u|^{p}(y)\\,dy\\right]+\\nabla\\cdot\\left(A(x)\\nabla u(x)\\right),\\qquad \\text{in}\\quad \\R^+\\times\\O$$ where $\\O\\subset \\R^N$ is a bounded smooth domain, $k(.,.) \\in C(\\bar \\O \\times C(\\bar\\O), \\R), p\\ge 1$ and $A(x)$ is a smooth elliptic matrix. In a blind competition situation, i.e $K(x,y)=k(y)$, we show the existence of a unique positive steady state which is positively globally stable. That"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6471","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"}