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dc.contributor.authorCARRILLO, JOSÉ ANTONIO
dc.contributor.authorHITTMEIR, SABINE
dc.contributor.authorJÜNGEL, ANSGAR
dc.date.accessioned2016-02-25T12:58:31Z
dc.date.available2016-02-25T12:58:31Z
dc.date.issued2012-12
dc.identifier.citationCARRILLO JA, HITTMEIR S, JÜNGEL A (2012) CROSS DIFFUSION AND NONLINEAR DIFFUSION PREVENTING BLOW UP IN THE KELLER–SEGEL MODEL. Mathematical Models and Methods in Applied Sciences 22: 1250041. Available: http://dx.doi.org/10.1142/S0218202512500418.
dc.identifier.issn0218-2025
dc.identifier.issn1793-6314
dc.identifier.doi10.1142/S0218202512500418
dc.identifier.urihttp://hdl.handle.net/10754/597896
dc.description.abstractA parabolic-parabolic (Patlak-)Keller-Segel model in up to three space dimensions with nonlinear cell diffusion and an additional nonlinear cross-diffusion term is analyzed. The main feature of this model is that there exists a new entropy functional, yielding gradient estimates for the cell density and chemical concentration. For arbitrarily small cross-diffusion coefficients and for suitable exponents of the nonlinear diffusion terms, the global-in-time existence of weak solutions is proved, thus preventing finite-time blow up of the cell density. The global existence result also holds for linear and fast diffusion of the cell density in a certain parameter range in three dimensions. Furthermore, we show L∞ bounds for the solutions to the parabolic-elliptic system. Sufficient conditions leading to the asymptotic stability of the constant steady state are given for a particular choice of the nonlinear diffusion exponents. Numerical experiments in two and three space dimensions illustrate the theoretical results. © 2012 World Scientific Publishing Company.
dc.description.sponsorshipJ.A.C. was partially supported by the project MTM2011-27739-C04/-02 DGI (Spain) and 2009-SGR-345 from AGAUR-Generalitat de Catalunya. The work of S. H. was supported by Award No. KUK-I1-007-43, funded by King Abdullah University of Science and Technology (KAUST). S. H. and A.J. acknowledge partial support from the Austrian Science Fund (FWF), grants P20214, P22108, and I395; the Austrian-Croatian Project HR 01/2010 and the Austrian-French Project FR 07/2010 of the Austrian Exchange Service (OAD). All authors acknowledge support from the Austrian-Spanish Project ES 08/2010 of the OAD.
dc.publisherWorld Scientific Pub Co Pte Lt
dc.subjectBlow up
dc.subjectChemotaxis
dc.subjectCross-diffusion
dc.subjectDegenerate diffusion
dc.subjectGlobal existence of solution
dc.subjectKeller-Segel model
dc.titleCROSS DIFFUSION AND NONLINEAR DIFFUSION PREVENTING BLOW UP IN THE KELLER–SEGEL MODEL
dc.typeArticle
dc.identifier.journalMathematical Models and Methods in Applied Sciences
dc.contributor.institutionUniversidad Autonoma de Barcelona, Barcelona, Spain
dc.contributor.institutionTechnische Universitat Wien, Vienna, Austria
dc.contributor.institutionImperial College London, London, United Kingdom


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