Unbounded mass radial solutions for the Keller-Segel equation in the disk

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dc.contributor.authorBonheure, Denis
dc.contributor.authorCasteras, Jean Baptiste
dc.contributor.authorRoman, Carlos
dc.date.accessioned2024-01-10T13:10:17Z
dc.date.available2024-01-10T13:10:17Z
dc.date.issued2021
dc.description.abstractWe consider the boundary value problem
dc.description.abstract{-Delta u + u - lambda e(u) = 0 ,u > 0 in B-1(0)
dc.description.abstractpartial derivative(nu)u = 0 on partial derivative B-1(0),
dc.description.abstractwhose solutions correspond to steady states of the Keller-Segel system for chemotaxis. Here B-1(0) is the unit disk,. the outer normal to partial derivative B-1(0), and lambda > 0 is a parameter. We show that, provided lambda is sufficiently small, there exists a family of radial solutions u(lambda) to this system which blow up at the origin and concentrate on partial derivative B-1(0), as lambda -> 0. These solutions satisfy
dc.description.abstractlim(lambda -> 0) u lambda(0)/vertical bar in lambda vertical bar = 0 and 0 lim(lambda -> 0) 1/vertical bar in lambda vertical bar integral(B1(0)) (lambda eu lambda(x)) dx < infinity,
dc.description.abstracthaving in particular unbounded mass, as lambda -> 0.
dc.description.funderBonheure's research (FNRS)
dc.description.funderFrench National Research Agency (ANR)
dc.description.funderChilean National Agency for Research and Development (ANID) through FONDECYT Iniciacion
dc.description.funderKing Baudouin Foundation - Thelam Funds
dc.description.funderAdvanced ARC grant at ULB - Partial Differential Equations in interaction
dc.description.funderUniversite libre de Bruxelles
dc.fechaingreso.objetodigital2024-03-21
dc.format.extent30 páginas
dc.fuente.origenWOS
dc.identifier.doi10.1007/s00526-021-02081-8
dc.identifier.eissn1432-0835
dc.identifier.issn0944-2669
dc.identifier.urihttps://doi.org/10.1007/s00526-021-02081-8
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/77823
dc.identifier.wosidWOS:000685965500003
dc.information.autorucFacultad de Matemáticas; Román Parra, Carlos Patricio; S/I; 1099610
dc.issue.numero5
dc.language.isoen
dc.nota.accesocontenido parcial
dc.publisherSPRINGER HEIDELBERG
dc.revistaCALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
dc.rightsacceso restringido
dc.subjectSTATIONARY SOLUTIONS
dc.subjectSTEADY-STATES
dc.subjectSYSTEM
dc.titleUnbounded mass radial solutions for the Keller-Segel equation in the disk
dc.typeartículo
dc.volumen60
sipa.codpersvinculados1099610
sipa.indexWOS
sipa.trazabilidadCarga SIPA;09-01-2024
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