Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Explanation of spurt for a non-Newtonian fluid by a diffusion term

Authors: P. Brunovský and D. Ševčovič
Journal: Quart. Appl. Math. 52 (1994), 401-426
MSC: Primary 76A10; Secondary 35Q35, 73F15
DOI: https://doi.org/10.1090/qam/1292194
MathSciNet review: MR1292194
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  • [1] S. Angenent, J. Mallet-Paret, and L. A. Pelletier, Stable transition layers in a semilinear boundary value problems, J. Differential Equations 67, 212-242 (1987)
  • [2] H. Bellout, F. Bloom, and J. Nečas, Phenomenological behavior of multipolar viscous fluids, Quart. Appl. Math. 50, 559-583 (1992)
  • [3] A. V. Bhave, R. C. Armstrong, and R. A. Brown, Kinetic theory and rheology of dilute, nonhomogeneous polymer solutions, J. Chem. Phys. 87, 3024-3025 (1991)
  • [4] A. W. El-Kareh and G. L. Leal, Existence of solutions for all Deborah numbers for a non-Newtonian model modified to include diffusion, J. Non-Newtonian Fluid Mech. 33, 257-287 (1989)
  • [5] D. Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Math., vol. 840, Springer-Verlag, New York, 1981
  • [6] J. K. Hunter and M. Slemrod, Viscoelastic fluid flow exhibiting hysteretic phase changes, Phys. Fluids 26, 2345-2351 (1983)
  • [7] R. Kolkka and G. Ierley, Phase space analysis of the spurt phenomenon fluid for the Giesekus viscoelastic fluid model, J. Non-Newtonian Fluid Mech. 33, 305-323 (1989)
  • [8] R. Kolkka, D. Malkus, D. Hansen, G. Ierley, and R. Worthing, Spurt phenomena of the Johnson-Sagelman fluid and related models, J. Non-Newtonian Fluid Mech. 29, 303-325 (1988)
  • [9] Xiao-Biao Lin, Shadowing lemma and singularly perturbed boundary value problems, SIAM J. Appl. Math. 49, 26-54 (1989)
  • [10] D. S. Malkus, J. A. Nohel, and B. J. Plohr, Analysis of new phenomena in shear flow of non-Newtonian fluids, SIAM J. Appl. Math. 51, 899-929 (1991)
  • [11] D. S. Malkus, J. A. Nohel, and B. J. Plohr, Dynamics of shear flow of a non-Newtonian fluid, J. Comp. Phys. 87, 464-487 (1990)
  • [12] J. A. Nohel and R. L. Pego, Nonlinear stability and asymptotic behavior of shearing motions of a non-Newtonian fluid, SIAM J. Math. Anal. 24, 911-942 (1993)
  • [13] J. A. Nohel, R. L. Pego, and A. E. Tzavaras, Stability of discontinuous steady states in shearing motion of a non-Newtonian fluid, Proc. Roy. Soc. Edinburgh Sect. A 115, 39-59 (1990)
  • [14] M. Protter and H. F. Weinberger, Maximum principles in differential equations, Springer-Verlag, New York, 1984
  • [15] G. Vinogradov, A. Malkin, Yu. Yanovskii, E. Borisenkova, B. Yarlykov, and G. Berezhnaya, Viscoelastic properties and flow of narrow distribution polybutadienes and polyisoprenes, J. Polymer Sci. Part A-2 10, 1061-1084 (1972)
  • [16] G. F. Webb, Existence and asymptotic behavior for a strongly damped nonlinear wave equation, Canad. Math. J. 32, 631-643 (1980)

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DOI: https://doi.org/10.1090/qam/1292194
Article copyright: © Copyright 1994 American Mathematical Society

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