Dynamical modelling of phase transitions by means of viscoelasticity in many dimensions

[1]  Michael Renardy,et al.  Mathematical problems in viscoelasticity , 1987 .

[2]  S. Agmon,et al.  Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I , 1959 .

[3]  J. Lions,et al.  Non-homogeneous boundary value problems and applications , 1972 .

[4]  T. Valent,et al.  Boundary Value Problems of Finite Elasticity , 1988 .

[5]  Paolo Marcellini,et al.  Semicontinuity problems in the calculus of variations , 1980 .

[6]  Tosio Kato.  Perturbation theory for linear operators , 1966 .

[7]  Nicola Fusco,et al.  Semicontinuity problems in the calculus of variations , 1984 .

[8]  Jerrold E. Marsden,et al.  Quasiconvexity at the boundary, positivity of the second variation and elastic stability , 1984 .

[9]  George E. Andrews,et al.  On the existence of solutions to the equation , 1980 .

[10]  J. Clements,et al.  EXISTENCE THEOREMS FOR A QUASILINEAR EVOLUTION EQUATION , 1974 .

[11]  Daisuke Fujiwara,et al.  An L_r-theorem of the Helmholtz decomposition of vector fields , 1977 .

[12]  J. Maddocks,et al.  A model for twinning , 1986 .

[13]  Daniel B. Henry.  Geometric Theory of Semilinear Parabolic Equations , 1989 .

[14]  R. J. Diperna.  Convergence of approximate solutions to conservation laws , 1983 .

[15]  Milan Miklavčič,et al.  Stability for semilinear parabolic equations with noninvertible linear operator , 1985 .

[16]  J. Greenberg.  On the existence, uniqueness, and stability of solutions of the equation PP0Xtt = E(Xx)Xxx + κXxxt , 1969 .

[17]  J. Ball,et al.  Asymptotic behaviour and changes of phase in one-dimensional nonlinear viscoelasticity , 1982 .

[18]  Lawrence C. Evans,et al.  Some remarks concerning quasiconvexity and strong convergence , 1987, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[19]  M. Krasnosel’skiǐ,et al.  Integral operators in spaces of summable functions , 1975 .

[20]  W. Ziemer.  Weakly differentiable functions , 1989 .

[21]  Robert L. Pego,et al.  Phase transitions in one-dimensional nonlinear viscoelasticity: admissibility and stability , 1987 .

[22]  Jerrold E. Marsden,et al.  Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity , 1977 .

[23]  Avner Friedman,et al.  Systems of nonlinear wave equations with nonlinear viscosity. , 1988 .

[24]  F. Falk.  Ginzburg-Landau theory of static domain walls in shape-memory alloys , 1983 .

[25]  C. Dafermos.  The mixed initial-boundary value problem for the equations of nonlinear one-dimensional viscoelasticity , 1969 .

[26]  D. Fujiwara.  On the asymptotic behaviour of the Green operators for elliptic boundary problems and the pure imaginary powers of some second order operators , 1969 .

[27]  M. Potier-Ferry.  On the mathematical foundations of elastic stability theory. I. , 1982 .

[28]  Krumhansl,et al.  Dynamics of twin boundaries in martensites. , 1987, Physical review letters.

[29]  Initial-boundary value problems for the equation $u_{tt}=(\sigma (u_x))_x+(\alpha (u_x)u_{xt})_x+f$ , 1988 .

[30]  Hartmut Pecher.  On global regular solutions of third order partial differential equations , 1980 .

[31]  J. Ball,et al.  Fine phase mixtures as minimizers of energy , 1987 .

[32]  Avner Friedman,et al.  Partial differential equations , 1969 .

[33]  J. Sprekels,et al.  Existence of solutions for a mathematical model of structural phase transitions in shape memory alloys , 1988 .

[34]  Charles B. Morrey,et al.  QUASI-CONVEXITY AND THE LOWER SEMICONTINUITY OF MULTIPLE INTEGRALS , 1952 .

[35]  R. J. DiPerna.  Convergence of approximate solutions to conservation laws , 1983 .