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G. Andrews and J. M. Ball. Asymptotic behaviour and changes of phase in one-dimensional nonlinear viscoelasticity. J. Differential Eqns, 44:306–341, 1982.
J. M. Ball. Loss of the constraint in convex variational problems. In Analyse Mathématique et Applications; Contributions en l'Honneur de J.-L.Lions, pages 39–53, Gauthier-Villars, 1988.
J. M. Ball. Material instabilities and the calculus of variations. In M. E. Gurtin, editor, Phase transformations and material instabilities in solids, pages 1–20, Mathematics Research Center, University of Wisconsin, Academic Press, 1984.
J. M. Ball. Minimizing sequences in thermomechanics. In Proc. Meeting on ‘Finite Thermoelasticity', pages 45–54, Acaademia Nazionale dei Lincei, Roma, 1986.
J. M. Ball. On the asymptotic behaviour of generalized processes, with applications to nonlinear evolution equations. J. Differential Eqns, 27:224–265, 1978.
J. M. Ball. Saddle-point analysis for an ordinary differential equation in a Banach space, and an application to dynamic buckling of a beam. In R. W. Dickey, editor, Nonlinear Elasticity, pages 93–160, Mathematics Research Center, University of Wisconsin, Academic Press, 1973.
J. M. Ball and J. Carr. Asymptotic behaviour of solutions of the Becker-Döring equations for arbitrary initial data. Proc. Royal Soc. Edinburgh A, 108:109–116,1988.
J. M. Ball, J. Carr, and O. Penrose. The Becker-Döring cluster equations; basic properties and asymptotic behaviour of solutions. Comm. Math. Phys., 104:657–692, 1986.
J. M. Ball, P. J. Holmes, R. D. James, R. L. Pego, and P. Swart. to appear.
J. M. Ball and R. D. James. Fine phase mixtures as minimizers of energy. Arch. Rat. Mech. Anal., 100:13–52, 1987.
J. M. Ball and R. D. James. Proposed experimental tests of a theory of fine microstructure, and the two-well problem. to appear.
J. M. Ball and G. Knowles. Lyapunov functions for thermoelasticity with spatially varying boundary temperatures. Arch. Rat. Mech. Anal., 92:193–204, 1986.
J. M. Ball and M. Slemrod. Nonharmonic Fourier series and the stabilization of distributed bilinear control systems. Comm. Pure Appl. Math., 32:555–587, 1979.
E. A. Barbashin and N. N. Krasovskii. Stability of motion in the large. Dokl. Akad. Nauk SSSR, 86:453–456, 1952.
J. Carr. Dynamics of cluster growth. In this proceedings. [16] J. Carr and R. L. Pego. Metastable patterns in solutions of u t = ε2 u χχ − f (u). Comm. Pure Appl. Math., to appear.
M. Chipot and D. Kinderlehrer. Equilibrium configurations of crystals. Arch. Rat. Mech. Anal., 103:237–277, 1988.
B. D. Coleman and E. H. Dill. On thermodynamics and the stability of motion of materials with memory. Arch. Rat. Mech. Anal., 51:1–53, 1973.
C. M. Dafermos. Asymptotic behaviour of solutions of evolution equations. In M. G. Crandall, editor, Nonlinear Evolution Equations, pages 103–124, Mathematics Research Center, University of Wisconsin, Academic Press, 1978.
P. Duhem. Traité d'Énergetique ou de Thermodynamique Générale. Gauthier-Villars, Paris, 1911.
J. L. Ericksen. Thermoelastic stability. In Proc 5 th National Cong. Appl. Mech., pages 187–193, 1966.
I. Fonseca. Interfacial energy and the Maxwell rule. Arch. Rat. Mech. Anal., 106:63–95, 1989.
J. K. Hale. Dynamical systems and stability. J. Math. Anal. Appl., 26:39–59, 1969.
D. Henry. Geometric Theory of Semilinear Parabolic Equations. Volume 840 of Lecture Notes in Mathematics, Springer-Verlag, 1981.
J. P. LaSalle. The extent of asymptotic stability. Proc. Nat. Acad. Sci. USA, 46:363–365, 1960.
P. Lin. Maximization of the entropy for an elastic body free of surface traction. to appear.
S. Müller. Minimizing sequences for nonconvex functionals, phase transitions and singular perturbations. In this proceedings.
S. Müller. Strong convergence and arbitrarily slow decay of energy for a class of bilinear control problems. J. Differential Eqns, to appear.
G. P. Parry. On shear bands in crystals. J. Mech. Phys. Solids, 35:367–382, 1987.
R. L. Pego. Phase transitions in one-dimensional nonlinear viscoelasticity: admissibility and stability. Arch. Rat. Mech. Anal., 97:353–394, 1987.
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Ball, J.M. (1990). Dynamics and minimizing sequences. In: Kirchgässner, K. (eds) Problems Involving Change of Type. Lecture Notes in Physics, vol 359. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52595-5_81
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