One-dimensional chemotaxis kinetic model

Sharifi tabar, M ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1007/s00030-010-0088-8
  3. Abstract:
  4. In this paper, we study a variation of the equations of a chemotaxis kinetic model and investigate it in one dimension. In fact, we use fractional diffusion for the chemoattractant in the Othmar-Dunbar-Alt system (Othmer in J Math Biol 26(3):263-298, 1988). This version was exhibited in Calvez in Amer Math Soc, pp 45-62, 2007 for the macroscopic well-known Keller-Segel model in all space dimensions. These two macroscopic and kinetic models are related as mentioned in Bournaveas, Ann Inst H Poincaré Anal Non Linéaire, 26(5):1871-1895, 2009, Chalub, Math Models Methods Appl Sci, 16(7 suppl):1173-1197, 2006, Chalub, Monatsh Math, 142(1-2):123-141, 2004, Chalub, Port Math (NS), 63(2):227-250, 2006. The model we study here behaves in a similar way to the original model in two dimensions with the spherical symmetry assumption on the initial data which is described in Bournaveas, Ann Inst H Poincaré Anal Non Linéaire, 26(5):1871-1895, 2009. We prove the existence and uniqueness of solutions for this model, as well as a convergence result for a family of numerical schemes. The advantage of this model is that numerical simulations can be easily done especially to track the blow-up phenomenon
  5. Keywords:
  6. Chemotaxis ; Fractional diffusion ; Hilbert transform ; Keller-Segel model ; Kinetic model ; Numerical simulation ; Othmar-Dunbar-Alt system
  7. Source: Nonlinear Differential Equations and Applications ; Volume 18, Issue 2 , 2011 , Pages 139-172 ; 10219722 (ISSN)
  8. URL: http://link.springer.com/article/10.1007%2Fs00030-010-0088-8