References
J. M. Ball [1977] Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63, 337–403.
J. M. Ball [1984] Material instabilities and the calculus of variations, in “Phase Transformations and Material Instabilities in Solids”, ed. M. Gurtin, Academic Press.
J. M. Ball & G. Knowles [1985] in preparation.
J. M. Ball & F. Murat [1984] W1,p-quasiconvexity and variational problems for multiple integrals, J. Functional Analysis 58, 225–253.
O. Bolza [1904] “Lectures on the Calculus of Variations”, Reprinted by Chelsea, N.Y., 1973.
M. Chicco [1970] Principio di massimo per soluzioni di problemi al contorno misti per equazioni ellittiche di tipo variazionale, Boll. Unione Mat. Ital. (4) 3, 384–394.
B. D. Coleman & E. H. Dill [1973] On thermodynamics and the stability of motion of materials with memory, Arch. Rational Mech. Anal. 51, 1–53.
C. M. Dafermos [1983] Hyperbolic systems of conservation laws, in “Systems of Nonlinear Partial Differential Equations” ed. J. M. Ball, D. Reidel, 25–70.
P. Duhem [1911] “Traité d'Enérgetique ou de Thermodynamique Générale”, GauthierVillars, Paris.
J. L. Ericksen [1966] Thermoelastic stability, Proc. 5th National Cong. Appl. Mech. 187–193.
W. L. Kath & D. S. Cohen [1982] Waiting-time behavior in a nonlinear diffusion equation, Studies in Applied Math. 67, 79–105.
P. Hartman [1964] “Ordinary Differential Equations”, John Wiley & Sons, New York, reprinted by Birkhauser, Boston, 1982.
E. W. Larsen & G. C. Pomraning [1980] Asymptotic analysis of nonlinear Marshak waves, SIAM J. Appl. Math. 39, 201–212.
C-S. Man [1985] Dynamic admissible states, negative absolute temperature, and the entropy maximum principle, preprint.
M. Marcus & V. J. Mizel [1972] Absolute continuity on tracks and mappings of Sobolev spaces, Arch. Rational Mech. Anal. 45, 294–320.
C. B. Morrey [1966] “Multiple Integrals in the Calculus of Variations”, Springer.
F. Rothe [1984] “Global Solutions of Reaction-Diffusion Systems”, Springer Lecture Notes in Mathematics Vol. 1072.
N. Trudinger [1977] Maximum principles for linear, non-uniformly elliptic operators with measurable coefficients, Math. Zeitschrift 156, 291–301.
C. Truesdell [1984] “Rational Thermodynamics”, 2nd edition, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo.
Y. B. Zeldovich & Y. P. Raizer [1969], “Physics of Shock Waves & High Temperature Hydrodynamic Phenomena”, vol. II, Academic Press, New York.
Author information
Authors and Affiliations
Additional information
Dedicated to James Serrin on the occasion of his 60th birthday
Rights and permissions
About this article
Cite this article
Ball, J.M., Knowles, G. Lyapunov functions for thermomechanics with spatially varying boundary temperatures. Arch. Rational Mech. Anal. 92, 193–204 (1986). https://doi.org/10.1007/BF00254826
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00254826