Young measure solutions for nonlinear evolutionary systems of mixed type

Sophia Demoulini

Annales de l'I.H.P. Analyse non linéaire (1997)

  • Volume: 14, Issue: 1, page 143-162
  • ISSN: 0294-1449

How to cite

top

Demoulini, Sophia. "Young measure solutions for nonlinear evolutionary systems of mixed type." Annales de l'I.H.P. Analyse non linéaire 14.1 (1997): 143-162. <http://eudml.org/doc/78404>.

@article{Demoulini1997,
author = {Demoulini, Sophia},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {hyperbolic-elliptic; dispersive-parabolic; time-discretisation},
language = {eng},
number = {1},
pages = {143-162},
publisher = {Gauthier-Villars},
title = {Young measure solutions for nonlinear evolutionary systems of mixed type},
url = {http://eudml.org/doc/78404},
volume = {14},
year = {1997},
}

TY - JOUR
AU - Demoulini, Sophia
TI - Young measure solutions for nonlinear evolutionary systems of mixed type
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1997
PB - Gauthier-Villars
VL - 14
IS - 1
SP - 143
EP - 162
LA - eng
KW - hyperbolic-elliptic; dispersive-parabolic; time-discretisation
UR - http://eudml.org/doc/78404
ER -

References

top
  1. [1] J. Ball, A version of the fundamental theorem of Young measures, in PDE's and continuum models of phase transitions, Rascle, Serre and Slemrod, eds., Vol. 344, Lecture Notes of Physics, Springer-Verlag, 1989, pp. 207-215. Zbl0991.49500MR1036070
  2. [2] J. Ball, P. Holmes, R. James, R. Pego and P. Swart, On the dynamics of fine structure, J. Nonlinear Science Vol. 1, 1991, pp. 17-70. Zbl0791.35030MR1102830
  3. [3] F. Bethuel, J. Coron, J. Ghidaglia and A. Soyeur, Heat flows and relaxed energies for harmonic maps, in Nonlinear Diffusion Equations and Their Equilibrium States, 3, Lloyd, Ni, Peletier and Serrin, eds., Progress in Nonlinear Differential Equations, Vol. 7, Birkhäuser, 1992, pp. 99-109. Zbl0795.35053MR1167832
  4. [4] M. Chipot and D. Kinderlehrer, Equilibrium Configurations of Crystals, Arch. Rat. Mech. Anal., Vol. 103 (3), 1988, pp. 237-277. Zbl0673.73012MR955934
  5. [5] B. Dacorogna, Direct Methods in the Calculus of Variations, Springer-Verlag, 1989. Zbl0703.49001MR990890
  6. [6] S. Demoulini, Young measure solutions for a nonolinear parabolic equation of forward-backward type, SIAM J. Math. Anal., Vol. 27 (2), 1996, pp. 376-403. Zbl0851.35066MR1377480
  7. [7] R. Diperna, Convergence of approximate solutions to conservation laws, Arch. Rat. Mech. Anal., Vol. 82, 1983, pp. 27-70. Zbl0519.35054MR684413
  8. [8] R. Diperna, Measure-valued solutions to conservation laws, Arch. Rat. Mech. Anal., Vol. 88 (3), 1985, pp. 223-270. Zbl0616.35055MR775191
  9. [9] H.T. Fan and M. Slemrod, Shock induced transitions and phase structures in general media, Dunn, Fosdick and Slemrod, eds., IMA Volumes in Mathematics and its Applications, Vol. 52, Springer Verlag, 1993. Zbl0807.76031MR1240329
  10. [10] K. Horihata and N. Kikuchi, A construction of solutions satisfying a Cacciopoli inequality for non-linear parabolic equations associated to a variational functional of harmonic type, Boll. Un. Mat. Ital. Vol. 3-A(7), 1989, pp. 199-207. 
  11. [11] ] D. Kinderlehrer and P. Pedregal, Weak convergence of integrands and the Young measure representation, Siam. J. Math. Anal., Vol. 23 (1), 1992, pp. 1-19. Zbl0757.49014MR1145159
  12. [12] D. Kinderlehrer and P. Pedregal, Remarks about the analysis of Gradient Young measures, J. Geom. Anal., Vol. 4 (1), 1994, pp. 59-90. Zbl0808.46046MR1274138
  13. [13] J.L. Lions, Quelques methodes de resolution des problemes aux limites non lineaires, Dunod, 1969. Zbl0189.40603MR259693
  14. [14] P. Rybka, Dynamical modeling of phase transitions by means of viscoelasticity in many dimensions, Proc. Roy. Soc. Edinburgh, Vol. 121A (1-2), 1993, pp. 101-138. Zbl0758.73004MR1169897
  15. [15] M. Slemrod, Dynamics of measure valued solutions to a backward-forward heat equation, J. Dynamics Diff. Equations, Vol. 3 (1), 1991, pp. 1-28. Zbl0747.35013MR1094722
  16. [16] P. Swart and P. Holmes, Energy minimisation and formation of microstructure in dynamic anti-plane shear, Arch. Rat. Mech. Anal., Vol. 121 (1), 1992, pp. 37-85. Zbl0786.73066MR1185570

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.