Article PDF
Avoid common mistakes on your manuscript.
References
Ericksen, J. L., A thermo-kinetic view of elastic stability theory. Int. J. Solids Structures 2, 573–580 (1966).
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).
Gurtin, M. E., Thermodynamics and stability. Arch. Rational Mech. Analysis 59, 63–96 (1975).
Volpert, A. I., The space BV and quasilinear equations. Mat. Sbornik (N.S.) 73(115), 255–302 (1967). English transl. Math. USSR-Sbornik 2, 225–267 (1967).
Liu, T.-P., Initial-boundary value problems for gas dynamics. Arch. Rational Mech. Analysis 64, 137–168 (1977).
Coleman, B. D., & W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Rational Mech. Analysis 13, 167–178 (1963).
Liu, T.-P., The entropy condition and the admissibility of shocks. J. Math. Anal. Appl. 53, 78–88 (1976).
Dafermos, C. M., The entropy rate admissibility criterion in thermoelasticity. Rend. Accad. Naz. Lincei, Ser. VIII, 57, 113–119 (1974).
Serrin, J., The concepts of thermodynamics. Contemporary Developments in Continuum Mechanics and Partial Differential Equations (G. Dela Penha & L. Medeiros Eds.). North Holland 1978.
Diperna, R. J., Uniqueness of solutions to hyperbolic conservation laws. Indiana U. Math. J. 28, 137–188 (1979).
Gibbs, J. W., Graphical methods in the thermodynamics of fluids I. Trans. Connecticut Acad. II, 309–342 (1873).
Knops, R. J., & E. W. Wilkes, Theory of Elastic Stability. Handbuch der Physik VIa/3. Berlin, Heidelberg, New York: Springer 1973.
Diperna, R. J., Singularities of solutions of nonlinear hyperbolic systems of conservation laws. Arch. Rational Mech. Analysis 60, 75–100 (1975).
Truesdell, C. A., & W. Noll, The Non-linear Field Theories of Mechanics. Handbuch der Physik III/3. Berlin, Heidelberg, New York: Springer 1965.
Ball, J. M., Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rational Mech. Analysis 63, 337–403 (1977).
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).
Ericksen, J. L., Special topics in elastostatics. Advances in Applied Mechanics 17. New York: Academic Press 1977.
Ball, J. M., Strict convexity, strong ellipticity, and the regularity of weak solutions to nonlinear variational problems (to appear).
Fichera, G., Existence Theorems in Elasticity. Handbuch der Physik VI a/2. Berlin, Heidelberg, New York: Springer 1972.
Author information
Authors and Affiliations
Additional information
Dedicated to Clifford Truesdell on the occasion of his sixtieth birthday
Rights and permissions
About this article
Cite this article
Dafermos, C.M. The second law of thermodynamics and stability. Arch. Rational Mech. Anal. 70, 167–179 (1979). https://doi.org/10.1007/BF00250353
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00250353