An existence and uniqueness theorem for incremental viscoelasticity
Authors:
R. Quintanilla and H. T. Williams
Journal:
Quart. Appl. Math. 43 (1985), 287-294
MSC:
Primary 73G15
DOI:
https://doi.org/10.1090/qam/814227
MathSciNet review:
814227
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Additional Information
- A. C. Pipkin and R. S. Rivlin, Small deformations superposed on large deformations in materials with fading memory, Arch. Rational Mech. Anal. 8 (1961), 297–308. MR 135755, DOI https://doi.org/10.1007/BF00277445
D. Iesan, Incremental equations in thermoelasticity, J. Therm. Stresses 3, 41–56 (1980)
- C. B. Navarro and R. Quintanilla, On existence and uniqueness in incremental thermoelasticity, Z. Angew. Math. Phys. 35 (1984), no. 2, 206–215 (English, with French summary). MR 756406, DOI https://doi.org/10.1007/BF00947933
H. T. Williams, Theory and applications of thermoviscoelasticity, Ph.D. Thesis. University of East Anglia, 1983
- P. Chadwick and R. W. Ogden, On the definition of elastic moduli, Arch. Rational Mech. Anal. 44 (1971/72), 41–53. MR 334655, DOI https://doi.org/10.1007/BF00250827
R. J. Knops and E. W. Wilkes, Theory of elastic stability, Handbuch der Physik, vol. VIa/3, C. Truesdell (Ed.), Springer, Berlin, 1973
- Carlos B. Navarro, On symmetry and monotonicity of relaxation functions in linear viscoelasticity, Z. Angew. Math. Phys. 30 (1979), no. 3, 541–547 (English, with French summary). MR 545896, DOI https://doi.org/10.1007/BF01588901
- Paul Germain and Bernard Nayroles (eds.), Applications of methods of functional analysis to problems in mechanics, Lecture Notes in Mathematics, vol. 503, Springer-Verlag, Berlin-New York, 1976. Joint Symposium, IUTAM/IMU, held in Marseille, September 1–6, 1975. MR 0521351
- Tosio Kato, Linear evolution equations of “hyperbolic” type. II, J. Math. Soc. Japan 25 (1973), 648–666. MR 326483, DOI https://doi.org/10.2969/jmsj/02540648
- S. Chiriţă, Uniqueness and continuous dependence results for the incremental thermoelasticity, J. Thermal Stresses 5 (1982), no. 2, 161–172. MR 695429, DOI https://doi.org/10.1080/01495738208942142
A. C. Pipkin and R. S. Rivlin, Small deformations superposed on large deformations in materials with fading memory, Arch. Rat. Mech. Anal. 8 297–308 (1961)
D. Iesan, Incremental equations in thermoelasticity, J. Therm. Stresses 3, 41–56 (1980)
C. B. Navarro and R. Quintanilla, On existence and uniqueness in incremental thermoelasticity, to appear in J App. Math. and Phys. (ZAMP)
H. T. Williams, Theory and applications of thermoviscoelasticity, Ph.D. Thesis. University of East Anglia, 1983
P. Chadwick and R. W. Ogden, On the definition of elastic moduli, Arch. Rat. Mech. Anal. 44 41–53 (1971)
R. J. Knops and E. W. Wilkes, Theory of elastic stability, Handbuch der Physik, vol. VIa/3, C. Truesdell (Ed.), Springer, Berlin, 1973
C. B. Navarro, On symmetry and monotinicity of relaxation functions in linear viscoelasticity, J. App. Math. and Phys. (ZAMP) 30, 541–546 (1979)
C. M. Dafermos, Contraction semigroups and trend to equilibrium in continuum mechanics, IUTAM/IMU Symp. on Applications of Methods of Functional Analysis to Problems in Mechanics, P. Germain and B Nayroles (Eds.), Lecture Notes in Math. 503, Springer, Berlin, pp. 295–306, 1976
T. Kato, Linear evolution equations of the hyperbolic type, II, J. Math. Soc. Japan, 5 (1973)
S. Chirita, Uniqueness and continuous dependence results for the incremental thermoelasticity, J. Therm. Stresses 5, 161–172 (1982)
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© Copyright 1985
American Mathematical Society
