The minimum free energy for a class of compressible viscoelastic fluids

Advances in Differential Equations

Volumn 7, Issue 3, 2002, Pages 319-342

  Fabrizio, M ^a   Gentili, G ^a   Golden, J M ^b  

^a UNIVERSITY OF BOLOGNA   (Italy)

^b DUBLIN INSTITUTE OF TECHNOLOGY   (Ireland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1342311720     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. B.D. Coleman and D. R. Owen, A mathematical foundation for thermodynamics, Arch. Rational Mech. Anal., 54 (1974), 1-104.
2. W.A. Day, Reversibility, recoverable work and free energy in linear viscoelasticity, Quart. J. Mech. Appl. Math., 23 (1970), 1-15.
3. W.A. Day, The thermodynamics of materials with memory, in "Materials with Memory," ed. D. Graffi, Liguori, Naples, 1979.
4. L. Deseri, G. Gentili, and J.M. Golden, An explicit formula for the minimum free energy in linear viscoelasricity, J. of Elasticity, 54 (1999), 141-185.
5. G. Gentili, Free energy and domain of dependence for weakly compressible viscoelastic fluids, Diff. and Integral Equations, 10 (1997), 757-776.
6. J.M. Golden, Free energies in the frequency domain: the scalar case, Quart. Appl. Math., 58 (2000), 127-150.
7. M. Fabrizio, C. Giorgi, and A. Morro, Free energies and dissipation properties for systems with memory, Arch. Rational Mech. Anal., 125 (1994), 341-373.
8. M. Fabrizio and J.M. Golden, Maximum and minimum free energies for a linear viscoelastic material, Quart. Appl. Math. (to appear).
9. M. Fabrizio and B. Lazzari, On asymptotic stability for linear viscoelastic fluids, Diff. and Int. Eq., 6 (1993), 491-505.
10. M. Fabrizio and A. Morro, "Mathematical Problems in Linear Viscoelasticity," SIAM, Philadelphia, 1992.
11. I.C. Gohberg and M.G. Kreǐn, Systems of integral equations on a half-line with kernels depending on the difference of arguments, Am. Math. Soc. Transl. Ser. 2, 14 (1960), 217-287.
12. P.R. Halmos, "Finite-Dimensional Vector Spaces," Springer-Verlag, New York, 1972
13. D.D. Joseph, "Fluid Dynamics of Viscoelastic Liquids," Applied Mathematical Sciences, Springer-Verlag, 1990.
14. N.I. Muskhelishvili, "Singular Integral Equations," Noordhoff, Groningen, 1953.
15. W. Noll, A new mathematical theory of simple materials, Arch. Rational Mech. Anal., 48 (1972), 1-50.
16. I.N. Sneddon, "The Use of Integral Transforms," McGraw-Hill, New York, 1972.
17. E.C. Titchmarsh, "Introduction to the Theory of Fourier Integrals," Clarendon, Oxford, 1937.