Free Access
Issue
Math. Model. Nat. Phenom.
Volume 6, Number 5, 2011
Complex Fluids
Page(s) 84 - 97
DOI https://doi.org/10.1051/mmnp/20116505
Published online 10 August 2011
  1. J. W. Barret, C. Schwab, E. Süli. Existence of global weak solutions for some polymeric flow models. Math. Model. Meth. Appl. Sci., 15 (2005), No. 6, 939–983. [CrossRef] [MathSciNet] [Google Scholar]
  2. R. B. Bird, R. C. Armstrong, O. Hassager. Dynamics of Polymeric Liquids, Vol. 1: Fluid Mechanics. J. Wiley & Sons, New York, 1987. [Google Scholar]
  3. R. B. Bird, R. C. Armstrong, O. Hassager. Dynamics of Polymeric Liquids, Vol. 2: Kinetic Theory. J. Wiley & Sons, New York, 1987. [Google Scholar]
  4. A. V. Busuioc, I. S. Ciuperca, D. Iftimie and L. I. Palade. The FENE dumbbell polymer model: existence and uniqueness of solutions for the momentum balance equation. Journal of Dynamics and Differential Equations, submitted, 2011. [Google Scholar]
  5. J. A. Carillo, S. Cordier, S. Mancini. A decision-making Fokker-Planck model in computational neuroscience. To appear in Journal of Mathematical Biology, 2011. [Google Scholar]
  6. L. Chupin. The FENE model for viscoelastic thin film flow. Methods Appl. Anal., 16 (2009), No. 2, 217–261. [MathSciNet] [Google Scholar]
  7. I. S. Ciuperca, L. I. Palade. The steady state configurational distribution diffusion equation of the standard FENE dumbbell polymer model: existence and uniqueness of solutions for arbitrary velocity gradients. Mathematical Models & Methods in Applied Sciences, 19 (2009), 2039–2064. [CrossRef] [MathSciNet] [Google Scholar]
  8. I. S. Ciupercă, L. I. Palade. On the existence and uniqueness of solutions of the configurational probability diffusion equation for the generalized rigid dumbbell polymer model. Dynamics of Partial Differential Equations, 7 (2010), 245–263. [MathSciNet] [Google Scholar]
  9. Q. Du, C. Liu, P. Yu. FENE dumbbell model and its several linear and nonlinear closure approximations. Multiscale Model. Simul., 4 (2005), No. 3, 709–731. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed] [Google Scholar]
  10. D. Henry. Geometric Theory of semilinear parabolic equations. Lecture notes in mathematics, Vol. 840. Springer Verlag, New York, 1981. [Google Scholar]
  11. R. R. Huilgol, N. Phan-Thien. Fluid Mechanics of Viscoelasticity. Elsevier, Amsterdam, 1997. [Google Scholar]
  12. B. Jourdain, C. Le Bris, T. Lelièvre, F. Otto. Long-time asymptotics of a multiscale model for a polymeric fluid flows. Arch. Rational Mech. Anal., 181 (2006), 97–148. [CrossRef] [MathSciNet] [Google Scholar]
  13. J. G. Kirkwood. Macromolecules, edited by P. L. Auer. Gordon and Breach, 1968. [Google Scholar]
  14. R. G. Larson. Constitutive Equations for Polymer Melts and Solutions. Butterworths, Boston, 1988. [Google Scholar]
  15. F. Lin, P. Zhang, Z. Zhang. On the global existence of smooth solution to the 2-D FENE Dumbell Model. Commun. Math. Phys., 277 (2008), 531–553. [CrossRef] [Google Scholar]
  16. N. Masmoudi. Well-Posedness for the FENE dumbbell model of polymeric flows. Comm. Pure Appl. Math., 61 (2008), No. 12, 1685–1714. [CrossRef] [MathSciNet] [Google Scholar]
  17. F. A. Morrison. Understanding Rheology. Oxford University Press, Oxford, 2001. [Google Scholar]
  18. J. Nečas. Les méthodes directes en théorie des équations elliptiques. Masson, Paris, 1967. [Google Scholar]
  19. S. Cleja-Ţigoiu, V. Ţigoiu. Rheology and Thermodynamics, Part I - Rheology. Editura Universităţii din Bucureşti, Bucureşti, 1998. [Google Scholar]
  20. V. A. Volpert, A. I. Volpert. Location of spectrum and stability of solutions for monotone parabolic system. Advances in Differential Equations, 2 (1997), No. 5, 811–830. [MathSciNet] [Google Scholar]
  21. H. Zhang, P. Zhang. Local existence for the FENE-dumbbell model of polymeric fluids. Arch. Ratl. Mech. Anal., 181 (2006), 373–400. [CrossRef] [MathSciNet] [Google Scholar]

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