Young measure solutions for nonlinear evolutionary systems of mixed type
Demoulini, Sophia
Annales de l'I.H.P. Analyse non linéaire, Tome 14 (1997), p. 143-162 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPC_1997__14_1_143_0,
     author = {Demoulini, Sophia},
     title = {Young measure solutions for nonlinear evolutionary systems of mixed type},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {14},
     year = {1997},
     pages = {143-162},
     mrnumber = {1437192},
     zbl = {0871.35065},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1997__14_1_143_0}
}

Demoulini, Sophia. Young measure solutions for nonlinear evolutionary systems of mixed type. Annales de l'I.H.P. Analyse non linéaire, Tome 14 (1997) pp. 143-162. http://gdmltest.u-ga.fr/item/AIHPC_1997__14_1_143_0/

[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. | MR 1036070 | Zbl 0991.49500

[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. | MR 1102830 | Zbl 0791.35030

[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. | MR 1167832 | Zbl 0795.35053

[4] M. Chipot and D. Kinderlehrer, Equilibrium Configurations of Crystals, Arch. Rat. Mech. Anal., Vol. 103 (3), 1988, pp. 237-277. | MR 955934 | Zbl 0673.73012

[5] B. Dacorogna, Direct Methods in the Calculus of Variations, Springer-Verlag, 1989. | MR 990890 | Zbl 0703.49001

[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. | MR 1377480 | Zbl 0851.35066

[7] R. Diperna, Convergence of approximate solutions to conservation laws, Arch. Rat. Mech. Anal., Vol. 82, 1983, pp. 27-70. | MR 684413 | Zbl 0519.35054

[8] R. Diperna, Measure-valued solutions to conservation laws, Arch. Rat. Mech. Anal., Vol. 88 (3), 1985, pp. 223-270. | MR 775191 | Zbl 0616.35055

[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. | MR 1240329 | Zbl 0807.76031

[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] ] 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. | MR 1145159 | Zbl 0757.49014

[12] D. Kinderlehrer and P. Pedregal, Remarks about the analysis of Gradient Young measures, J. Geom. Anal., Vol. 4 (1), 1994, pp. 59-90. | MR 1274138 | Zbl 0808.46046

[13] J.L. Lions, Quelques methodes de resolution des problemes aux limites non lineaires, Dunod, 1969. | MR 259693 | Zbl 0189.40603

[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. | MR 1169897 | Zbl 0758.73004

[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. | MR 1094722 | Zbl 0747.35013

[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. | MR 1185570 | Zbl 0786.73066