Analysis of a one-dimensional variational model of the equilibrium shapel of a deformable crystal

Eric Bonnetier; Richard S. Falk; Michael A. Grinfeld

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1999)

  • Volume: 33, Issue: 3, page 573-591
  • ISSN: 0764-583X

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Bonnetier, Eric, Falk, Richard S., and Grinfeld, Michael A.. "Analysis of a one-dimensional variational model of the equilibrium shapel of a deformable crystal." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 33.3 (1999): 573-591. <http://eudml.org/doc/193936>.

@article{Bonnetier1999,
author = {Bonnetier, Eric, Falk, Richard S., Grinfeld, Michael A.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {minimization of nonconvex nonlocal functional; equilibrium configurations; one-dimensinal variational model; bulk energy; deformable crystal; surface energy; stable absolute minimum; minimizing sequence},
language = {eng},
number = {3},
pages = {573-591},
publisher = {Dunod},
title = {Analysis of a one-dimensional variational model of the equilibrium shapel of a deformable crystal},
url = {http://eudml.org/doc/193936},
volume = {33},
year = {1999},
}

TY - JOUR
AU - Bonnetier, Eric
AU - Falk, Richard S.
AU - Grinfeld, Michael A.
TI - Analysis of a one-dimensional variational model of the equilibrium shapel of a deformable crystal
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1999
PB - Dunod
VL - 33
IS - 3
SP - 573
EP - 591
LA - eng
KW - minimization of nonconvex nonlocal functional; equilibrium configurations; one-dimensinal variational model; bulk energy; deformable crystal; surface energy; stable absolute minimum; minimizing sequence
UR - http://eudml.org/doc/193936
ER -

References

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  1. [1] J. M. Ball and V. J. Mizel, One-dimensional variational problems whose minimizers do not satisfy the Euler Lagrange equation.Arch. Rational Mech. Anal 90 (1985) 325-388. Zbl0585.49002MR801585
  2. [2] C. Bandle, Isoperimetric Inequalities and Applications. Pitman (1980). Zbl0436.35063MR572958
  3. [3] B. Dacorogna, Direct Methods in the Calculus of Variations. Springer-Verlag, Berlin, New York (1989). Zbl0703.49001MR990890
  4. [4] Solids Far From Equilibrium. C. Godresche Ed., Cambridge University Press (1991). 
  5. [5] J. W. Gibbs, On the equilibrium of heterogeneous substances. Trans. Connect. Acad. Sci. 3 (1876-1878) 108-248, 343-524. JFM08.0559.03
  6. [6] E. Giusti, Minimal surfaces and functions of bounded variation. Birkhauser, Boston (1984). Zbl0545.49018MR775682
  7. [7] M. A. Grinfeld, Thermodynamic Methods in the Theory of Heterogeneous Systems. Longman (1991). Zbl0752.73001MR1243876
  8. [8] M. A. Grinfeld, Stress driven instabilities in crystals: mathematical models and physical manifestations. J. Nonlinear Sci. 3 (1993) 35-83. Zbl0843.73040MR1216987
  9. [9] M. A. Grinfeld, Manifestations of the stress driven rearrangement instabilities in creep, damaging and fracture. Final Report.Wright-Patterson Laboratory (1995). 
  10. [10] MSR Bulletin (1996). 
  11. [11] L. D. Landau and E. M. Lifshitz, Statistical physics, Part 1. Oxford, Pergamon Press (1986). Zbl0080.19702MR884707JFM64.0887.01
  12. [12] P. Nozières, Lectures at Collège de France (1988) unpublished notes. Growth and Shape of Crystals (lectures given at Beg-Rohu Summer School, Brittany, 1989) in Solids Far From Equilibrium, C. Godreche Ed., Cambridge University Press (1991). 
  13. [13] P. Nozières, Amplitude Expansion for the Grinfeld Instability due to Uniaxial Stress at a Solid Surface. J. Phys. 3 (1993) 681. 

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