|
Online ISSN 1552-4485; Print ISSN 0033-569X
On heat conduction in materials with memory
Author:
Jace W. Nunziato
Journal:
Quart. Appl. Math. 29 (1971), 187-204
MSC:
Primary 80.35
DOI:
https://doi.org/10.1090/qam/295683
MathSciNet review:
295683
Full-text PDF Free Access
References | Similar Articles | Additional Information
-
J. B. Brown, D. Y. Chung and P. W. Matthews, Heat pulses at low temperatures, Phys. Letters 21, 241–243 (1966)
- Carlo Cattaneo, Sulla conduzione del calore, Atti Sem. Mat. Fis. Univ. Modena 3 (1949), 83–101 (Italian). MR 0032898
- Peter J. Chen, On the growth and decay of one-dimensional temperature rate waves, Arch. Rational Mech. Anal. 35 (1969), no. 1, 1–15. MR 1553538, DOI https://doi.org/10.1007/BF00248491 P. J. Chen, On the growth and decay of temperature rate waves of arbitrary form, Z. Angew. Math. Phys. 20, 448–453 (1969)
- Bernard D. Coleman, Thermodynamics of materials with memory, Arch. Rational Mech. Anal. 17 (1964), 1–46. MR 171419, DOI https://doi.org/10.1007/BF00283864
- 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 Morton E. Gurtin, Equipresence and constitutive equations for rigid heat conductors, Z. Angew. Math. Phys. 18 (1967), 199–208 (English, with German summary). MR 214334, DOI https://doi.org/10.1007/BF01596912
- Bernard D. Coleman and Victor J. Mizel, Thermodynamics and departures from Fourier’s law of heat conduction, Arch. Rational Mech. Anal. 13 (1963), 245–261. MR 151119, DOI https://doi.org/10.1007/BF01262695
- 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
- Bernard D. Coleman and Walter Noll, An approximation theorem for functionals, with applications in continuum mechanics, Arch. Rational Mech. Anal. 6 (1960), 355–370 (1960). MR 119598, DOI https://doi.org/10.1007/BF00276168
- 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 and Walter Noll, Simple fluids with fading memory, Second-order Effects in Elasticity, Plasticity and Fluid Dynamics (Internat. Sympos., Haifa, 1962) Jerusalem Academic Press, Jerusalem; Pergamon, Oxford, 1964, pp. 530–552. MR 0163526
- W. A. Day and Morton E. Gurtin, On the symmetry of the conductivity tensor and other restrictions in the nonlinear theory of heat conduction, Arch. Rational Mech. Anal. 33 (1969), no. 1, 26–32. MR 1553529, DOI https://doi.org/10.1007/BF00248154
- W. S. Edelstein and M. E. Gurtin, Uniqueness theorems in the linear dynamic theory of anisotropic viscoelastic solids, Arch. Rational Mech. Anal. 17 (1964), 47–60. MR 180015, DOI https://doi.org/10.1007/BF00283865
- Morton E. Gurtin, On the thermodynamics of materials with memory, Arch. Rational Mech. Anal. 28 (1968), no. 1, 40–50. MR 1553503, DOI https://doi.org/10.1007/BF00281562
- M. E. Gurtin and I. Herrera, On dissipation inequalities and linear viscoelasticity, Quart. Appl. Math. 23 (1965), 235–245. MR 189346, DOI https://doi.org/10.1090/S0033-569X-1965-0189346-9
- Morton E. Gurtin and A. C. Pipkin, A general theory of heat conduction with finite wave speeds, Arch. Rational Mech. Anal. 31 (1968), no. 2, 113–126. MR 1553521, DOI https://doi.org/10.1007/BF00281373
- Oliver Dimon Kellogg, Foundations of potential theory, Die Grundlehren der Mathematischen Wissenschaften, Band 31, Springer-Verlag, Berlin-New York, 1967. Reprint from the first edition of 1929. MR 0222317 J. C. Maxwell, On the dynamical theory of gases, Philos. Trans. Roy. Soc. London 157, 49–88 (1867)
- V. J. Mizel and C.-C. Wang, A fading memory hypothesis which suffices for chain rules, Arch. Rational Mech. Anal. 23 (1966), 124–134. MR 210344, DOI https://doi.org/10.1007/BF00251728
- C. Truesdell and R. Toupin, The classical field theories, Handbuch der Physik, Bd. III/1, Springer, Berlin, 1960, pp. 226–793; appendix, pp. 794–858. With an appendix on tensor fields by J. L. Ericksen. MR 0118005
Retrieve articles in Quarterly of Applied Mathematics with MSC: 80.35
Retrieve articles in all journals with MSC: 80.35
Additional Information
Article copyright:
© Copyright 1971
American Mathematical Society