An existence and uniqueness theorem in quasi-static viscoelasticity
Author:
Mauro Fabrizio
Journal:
Quart. Appl. Math. 47 (1989), 1-8
MSC:
Primary 73F15; Secondary 35Q20, 73F05
DOI:
https://doi.org/10.1090/qam/987890
MathSciNet review:
987890
Full-text PDF Free Access
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Additional Information
- Gaetano Fichera, Avere una memoria tenace crea gravi problemi, Arch. Rational Mech. Anal. 70 (1979), no. 2, 101–112 (Italian). MR 1553577, DOI https://doi.org/10.1007/BF00250347
G. Fichera, Sul Principio della memoria evanescente, Rend. Sem. Mat. Univ. Padova 68, 245–259 (1982)
- Bernard D. Coleman and Walter Noll, Foundations of linear viscoelasticity, Rev. Modern Phys. 33 (1961), 239–249. MR 0158605, DOI https://doi.org/10.1103/RevModPhys.33.239
- Bernard D. Coleman, On thermodynamics, strain impulses, and viscoelasticity, Arch. Rational Mech. Anal. 17 (1964), 230–254. MR 171420, DOI https://doi.org/10.1007/BF00282439
- Bernard D. Coleman and Victor J. Mizel, Norms and semi-groups in the theory of fading memory, Arch. Rational Mech. Anal. 23 (1966), 87–123. MR 210343, DOI https://doi.org/10.1007/BF00251727
- M. Fabrizio and A. Morro, Viscoelastic relaxation functions compatible with thermodynamics, J. Elasticity 19 (1988), no. 1, 63–75. MR 928727, DOI https://doi.org/10.1007/BF00041695
- A. Morro and M. Fabrizio, On uniqueness in linear viscoelasticity: a family of counterexamples, Quart. Appl. Math. 45 (1987), no. 2, 321–325. MR 895102, DOI https://doi.org/10.1090/S0033-569X-1987-0895102-5
A. C. Pipkin, Lectures on viscoelasticity theory, Springer, Berlin, 1972
D. Graffi, Sui problemi della ereditarietà lineare, Nuovo Cimento 5, 53–71 (1928)
G. Fichera, Existence theorems in elasticity, Handbuch der Physik, vol. VI a/2, Springer, Heidelberg, 1972, pp. 347–389
- François Trèves, Basic linear partial differential equations, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1975. Pure and Applied Mathematics, Vol. 62. MR 0447753
M. S. Agranovich and M. I. Vishik, Elliptic boundary-value problems depending on a parameter, Dokl. Akad. Nauk SSSR 149, 223–226 (1963)
- William Alan Day, The thermodynamics of simple materials with fading memory, Springer-Verlag, New York-Heidelberg, 1972. Springer Tracts in Natural Philosophy, Vol. 22. MR 0366234
G. Fichera, Avere una memoria tenace crea gravi problemi, Arch. Rat. Mech. Anal. 70, 101–112 (1979)
G. Fichera, Sul Principio della memoria evanescente, Rend. Sem. Mat. Univ. Padova 68, 245–259 (1982)
B. D. Coleman and W. Noll, Foundations of linear viscoelasticity, Rev. Modern Phys. 33, 239–249 (1961)
B. D. Coleman, On thermodynamics, strain impulses, and viscoelasticity, Arch. Rat. Mech. Anal. 17, 230–254 (1964)
B. D. Coleman and V. J. Mizel, Norms and semi-groups in the theory of fading memory, Arch. Rat. Mech. Anal. 23, 87–123 (1966)
M. Fabrizio and A. Morro, Viscoelastic relaxation functions compatible with thermodynamics, J. Elasticity 19, 63–75 (1988)
A. Morro and M. Fabrizio, On uniqueness in linear viscoelasticity: A family of counterexamples, Quart. Appl. Math. 45, 321–325 (1987)
A. C. Pipkin, Lectures on viscoelasticity theory, Springer, Berlin, 1972
D. Graffi, Sui problemi della ereditarietà lineare, Nuovo Cimento 5, 53–71 (1928)
G. Fichera, Existence theorems in elasticity, Handbuch der Physik, vol. VI a/2, Springer, Heidelberg, 1972, pp. 347–389
F. Treves, Basic linear partial differential equations, Academic Press, New York, 1975
M. S. Agranovich and M. I. Vishik, Elliptic boundary-value problems depending on a parameter, Dokl. Akad. Nauk SSSR 149, 223–226 (1963)
W. A. Day, The thermodynamics of simple materials with fading memory, Springer Tracts in Natural Philosophy 22, Springer-Verlag, New York-Heidelberg, 1972
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Article copyright:
© Copyright 1989
American Mathematical Society