Powiadomienia systemowe
- Sesja wygasła!
Tytuł artykułu
Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
Keller-Segel chemotaxis model is described by a system of nonlinear partial differential equations: a convection diffusion equation for the cell density coupled with a reaction-diffusion equation for chemoattractant concentration. In this work, we study the phenomenon of Keller-Segel model coupled with Boussinesq equations. The main objective of this work is to study the global existence and uniqueness and boundedness of the weak solution for the problem, which is carried out by the Galerkin method.
Wydawca
Czasopismo
Rocznik
Tom
Strony
558--575
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
autor
- Department of Mathematics, Laboratory of Applied Mathematics and History and Didactics of Mathematiccs (LAMAHIS), University of 20 August 1955, Skikda, Algeria
autor
- Department of Mathematics, Laboratory of Applied Mathematics and History and Didactics of Mathematiccs (LAMAHIS), University of 20 August 1955, Skikda, Algeria
autor
- Department of Mathematics, Laboratory of Applied Mathematics and History and Didactics of Mathematiccs (LAMAHIS), University of 20 August 1955, Skikda, Algeria
Bibliografia
- [1] E. F. Keller and L. A. Segel, Initiation of slime mold aggregation viewed as an instability, J. Theor. Biol. 26 (1970), 399415.
- [2] M. D. Betterton and M. P. Brenner, Collapsing bacterial cylinders, Phys. Rev. E 64 (2001), 061904.
- [3] M. P. Brenner, L. S. Levitov, and E. O. Budrene, Physical mechanisms for chemotactic pattern formation by bacteria, Biophys. J. 74 (1998), no. 4, 1677–1693.
- [4] E. O. Budrene and H. C. Berg, Dynamics of formation of symmetrical patterns by chemotactic bacteria, Nature (London) 376 (1995), 49–53.
- [5] E. O. Budrene and H. C. Berg, Complex patterns formed by motile cells of Escherichia coli, Nature (London) 349 (1991), 630–633.
- [6] S. Childress and J. K. Percus, Nonlinear aspects of chemotaxis, Math. Biosci. 56 (1981), 217–237.
- [7] R. Duan, A. Lorz, and P. Markowich, Global solutions to the coupled Chemotaxis-Fluid equations, Comm. Partial Differential Equations 35 (2010), no. 9, 1635–1673.
- [8] M. A. Herrero, E. Medina, and J. J. L. Velazquez, Self-similar blow-up for a reactiondiffusion system, J. Comput. Appl. Math. 97 (1998), 99–119.
- [9] M. A. Herrero and J. J. L. Velazquez, A blow-up mechanism for a chemotaxis model, Ann. Scoula Norm. Pisa IV 35 (1997), 633–683.
- [10] M. A. Herrero, E. Medina, and J. J. L. Velazquez, Finite-time aggregation into a single point in a reaction-diffusion system, Nonlinearity 10 (1997), 1739–1754.
- [11] T. Hillen and A. Potapov, The one-dimensional chemotaxis model: global existence and asymptotic profile, Math. Methods Appl. Sci. 27 (2004), 1783–1801.
- [12] D. Horstmann and M. Winkler, Boundedness vs. blow-up in a chemotaxis system, J. Differential Equations 215 (2005), 52–107.
- [13] W. Jager and S. Luckhaus, On explosions of solutions to a system of partial differential equations modelling chemotaxis, Trans. Amer. Math. Soc. 329 (1992), 819–824.
- [14] A. Lorz, A coupled Keller-Segel model: Global existence for small initial data and blow-up delay, Commun. Math. Sci. 10 (2012), no. 2, 555–574.
- [15] C. Messikh, A. Guesmia, and S. Saadi, Global existence and uniqueness of the weak solution in Keller-Segel model, Glob. J. Sci. Front. Res. F Math. Decision Sci. 14 (2014), no. 2, 1–11.
- [16] T. Nagai, Blow-up of radially symmetric solutions to a chemotaxis system, Adv. Math. Sci. Appl. 5 (1995), 581–601.
- [17] K. Osaki and A. Yagi, Finite dimensional attractor for one-dimensional Keller-Segel equations, Funkcial. Ekvac. 44 (2001), 441–469.
- [18] A. Slimani, A. Rahai, A. Guesmia, and L. Bouzettouta, Stochastic chemotaxis model with fractional derivative driven by multiplicative noise, Int. J. Anal. Appl. 19 (2021), no. 6, 858–889, DOI: https://doi.org/10.28924/2291-8639-19-2021-858.
- [19] M. Mizuno and T. Ogawa, Regularity and asymptotic behavior for the Keller-Segel system of degenerate type with critical nonlinearity, J. Math. Sci. Univ. Tokyo 20 (2013), 375–433.
- [20] J.-G. Liu and A. Lorz, A coupled chemotaxis-fluid model: Global existence, Ann. I. H. Poincaré - AN 28 (2011), no. 5, 643–652.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-639fe64a-810d-41cb-971f-7360d53b242a