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Dafermos, C. M.

The second law of thermodynamics and stability. (English) Zbl 0448.73004

Arch. Ration. Mech. Anal. 70, 167-199 (1979).
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scan of Zbl 0448.73004

Cited in 12 Reviews
Cited in 220 Documents

MSC:

74A15 Thermodynamics in solid mechanics
74F05 Thermal effects in solid mechanics
80A05 Foundations of thermodynamics and heat transfer

Keywords:

relation between second law of thermodynamics and stability; Gauss-Green theorem; Clausius-Duhem inequality
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References:

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[2] Coleman, B. D., & E. H. Dill, On thermodynamics and the stability of motions of materials with memory. Arch. Rational Mech. Analysis 51, 1–13 (1973). · Zbl 0275.73003 · doi:10.1007/BF00275991
[3] Gurtin, M. E., Thermodynamics and stability. Arch. Rational Mech. Analysis 59, 63–96 (1975). · Zbl 0341.73003 · doi:10.1007/BF00281517
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[8] Dafermos, C. M., The entropy rate admissibility criterion in thermoelasticity. Rend. Accad. Naz. Lincei, Ser. VIII, 57, 113–119 (1974). · Zbl 0321.73001
[9] Serrin, J., The concepts of thermodynamics. Contemporary Developments in Continuum Mechanics and Partial Differential Equations (G. Dela Penha & L. Medeiros Eds.). North Holland 1978.
[10] Diperna, R. J., Uniqueness of solutions to hyperbolic conservation laws. Indiana U. Math. J. 28, 137–188 (1979). · Zbl 0409.35057 · doi:10.1512/iumj.1979.28.28011
[11] Gibbs, J. W., Graphical methods in the thermodynamics of fluids I. Trans. Connecticut Acad. II, 309–342 (1873).
[12] Knops, R. J., & E. W. Wilkes, Theory of Elastic Stability. Handbuch der Physik VIa/3. Berlin, Heidelberg, New York: Springer 1973. · Zbl 0377.73060
[13] Diperna, R. J., Singularities of solutions of nonlinear hyperbolic systems of conservation laws. Arch. Rational Mech. Analysis 60, 75–100 (1975). · Zbl 0324.35062 · doi:10.1007/BF00281470
[14] Truesdell, C. A., & W. Noll, The Non-linear Field Theories of Mechanics. Handbuch der Physik III/3. Berlin, Heidelberg, New York: Springer 1965. · Zbl 0779.73004
[15] Ball, J. M., Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rational Mech. Analysis 63, 337–403 (1977). · Zbl 0368.73040 · doi:10.1007/BF00279992
[16] Knowles, J. K., & E. Sternberg, On the failure of ellipticity of the equations for finite elastostatic plane strain. Arch. Rational Mech. Analysis 63, 321–336 (1977). · Zbl 0351.73061 · doi:10.1007/BF00279991
[17] Ericksen, J. L., Special topics in elastostatics. Advances in Applied Mechanics 17. New York: Academic Press 1977. · Zbl 0475.73017
[18] Ball, J. M., Strict convexity, strong ellipticity, and the regularity of weak solutions to nonlinear variational problems (to appear).
[19] Fichera, G., Existence Theorems in Elasticity. Handbuch der Physik VI a/2. Berlin, Heidelberg, New York: Springer 1972.
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