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
Full-text PDF Free Access
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Additional Information
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)
H. Bellout, F. Bloom, and J. Nečas, Phenomenological behavior of multipolar viscous fluids, Quart. Appl. Math. 50, 559–583 (1992)
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)
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)
D. Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Math., vol. 840, Springer-Verlag, New York, 1981
J. K. Hunter and M. Slemrod, Viscoelastic fluid flow exhibiting hysteretic phase changes, Phys. Fluids 26, 2345–2351 (1983)
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)
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)
Xiao-Biao Lin, Shadowing lemma and singularly perturbed boundary value problems, SIAM J. Appl. Math. 49, 26–54 (1989)
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)
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)
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)
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)
M. Protter and H. F. Weinberger, Maximum principles in differential equations, Springer-Verlag, New York, 1984
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)
G. F. Webb, Existence and asymptotic behavior for a strongly damped nonlinear wave equation, Canad. Math. J. 32, 631–643 (1980)
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)
H. Bellout, F. Bloom, and J. Nečas, Phenomenological behavior of multipolar viscous fluids, Quart. Appl. Math. 50, 559–583 (1992)
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)
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)
D. Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Math., vol. 840, Springer-Verlag, New York, 1981
J. K. Hunter and M. Slemrod, Viscoelastic fluid flow exhibiting hysteretic phase changes, Phys. Fluids 26, 2345–2351 (1983)
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)
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)
Xiao-Biao Lin, Shadowing lemma and singularly perturbed boundary value problems, SIAM J. Appl. Math. 49, 26–54 (1989)
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)
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)
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)
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)
M. Protter and H. F. Weinberger, Maximum principles in differential equations, Springer-Verlag, New York, 1984
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)
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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© Copyright 1994
American Mathematical Society
