{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:6FE6AQNPX67QOKMOHKMOYE42HK","short_pith_number":"pith:6FE6AQNP","schema_version":"1.0","canonical_sha256":"f149e041afbfbf07298e3a98ec139a3aa2682ec8ff09597d970ad13c4274e3c1","source":{"kind":"arxiv","id":"1308.6471","version":1},"attestation_state":"computed","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. 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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. 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