An evolutionary double-well problem
Tang, Qi ; Zhang, Kewei
Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007), p. 341-359 / Harvested from Numdam
@article{AIHPC_2007__24_3_341_0,
     author = {Tang, Qi and Zhang, Kewei},
     title = {An evolutionary double-well problem},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {24},
     year = {2007},
     pages = {341-359},
     doi = {10.1016/j.anihpc.2006.11.002},
     mrnumber = {2319937},
     zbl = {pre05225604},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2007__24_3_341_0}
}
Tang, Qi; Zhang, Kewei. An evolutionary double-well problem. Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) pp. 341-359. doi : 10.1016/j.anihpc.2006.11.002. http://gdmltest.u-ga.fr/item/AIHPC_2007__24_3_341_0/

[1] Acerbi E., Fusco N., Semi-continuity problems in the calculus of variations, Arch. Ration. Mech. Anal. 86 (1984) 125-145. | MR 751305 | Zbl 0565.49010

[2] Ball J.M., Convexity conditions and existence theorems in nonlinear elasticity, Arch. Ration. Mech. Anal. 63 (1977) 337-403. | MR 475169 | Zbl 0368.73040

[3] Ball J.M., A version of the fundamental theorem of Young measures, in: Rascle M., Serre D., Slemrod M. (Eds.), Partial Differential Equations and Continuum Models of Phase Transitions, Lecture Notes in Phys., vol. 334, Springer, Berlin, 1989, pp. 207-215. | MR 1036070 | Zbl 0991.49500

[4] Ball J.M., Continuity properties and global attractors of generalized semi-flows and the Navier-Stokes equations, J. Nonlinear Sci. 7 (5) (1997) 475-502. | Zbl 0903.58020

[5] Bhattacharya K., Firoozye N.B., James R.D., Kohn R.V., Restrictions on microstructures, Proc. Roy. Soc. Edinburgh Sect. A 124 (1994) 843-878. | MR 1303758 | Zbl 0808.73063

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

[7] Demoulini S., Weak solutions for a class of nonlinear systems of visco-elasticity, Arch. Ration. Mech. Anal. 155 (2000) 299-334. | MR 1808121 | Zbl 0991.74021

[8] Evans L.C., An unusual minimization principle for parabolic gradient flows, SIAM J. Math. Anal. 27 (1) (1996) 1-4. | MR 1373143 | Zbl 0857.35057

[9] Fuchs M., Regularity theorems for nonlinear systems of partial differential equations under natural ellipticity conditions, Analysis 7 (1987) 83-93. | MR 885719 | Zbl 0624.35032

[10] Giaquinta M., Introduction to Regularity Theory for Nonlinear Elliptic Systems, Birkhäuser, Basel, 1993. | MR 1239172 | Zbl 0786.35001

[11] Hale J., Asymptotic Behaviour of Dissipative Systems, Amer. Math. Soc., Providence, RI, 1988. | MR 941371 | Zbl 0642.58013

[12] Kohn R.V., The relaxation of a double-well energy, Cont. Mech. Therm. 3 (1991) 981-1000. | MR 1122017 | Zbl 0825.73029

[13] Kinderlehrer D., Pedregal P., Characterizations of Young measures generated by gradients, Arch. Ration. Mech. Anal. 115 (4) (1991) 329-365. | MR 1120852 | Zbl 0754.49020

[14] Kinderlehrer D., Pedregal P., Gradient Young measures generated by sequences in Sobolev spaces, J. Geom. Anal. 4 (1) (1994) 59-90. | MR 1274138 | Zbl 0808.46046

[15] J. Kristensen, Finite functionals and Young measures generated by gradients of Sobolev functions, Ph.D. Thesis, Technical University of Denmark, Lyngby, 1994.

[16] Morrey C.B., Multiple Integrals in the Calculus of Variations, Springer, 1966. | MR 202511 | Zbl 0142.38701

[17] Muller S., Sverak V., Unexpected solutions of first and second order partial differential equations, Special Volume Proc. ICM Volume II Documenta Math. (1998) 691-702. | MR 1648117 | Zbl 0896.35029

[18] M.O. Rieger, Young measure solutions for non-convex elasto-dynamics, Preprint. | Zbl 1039.74005

[19] Sverak V., Rank-one convexity does not imply quasi-convexity, Proc. Roy. Soc. Edinburgh Sect. A 120 (1992) 185-189. | MR 1149994 | Zbl 0777.49015

[20] Tang Q., Wang S., Time dependent Ginzburg-Landau equations of superconductivity, Physica D 88 (1995) 139-166. | MR 1360881 | Zbl 0900.35371

[21] Q. Tang, K.W. Zhang, Convergence of heat flow solutions under multi-well potential energy, Preprint.

[22] Zhang K.-W., On the Dirichlet problem for a class of quasilinear elliptic systems of partial differential equations in divergence form, in: Chern S.S. (Ed.), Partial Differential Equations, Proc. Sympos., Tianjin, 1986, Lecture Notes on Math., vol. 1306, Springer-Verlag, 1988, pp. 262-277. | MR 1032785 | Zbl 0672.35026

[23] Zhang K.W., Biting theorems for Jacobians and their applications, Ann. Inst. H. Poincaré 7 (1990) 345-365. | Numdam | MR 1067780 | Zbl 0717.49012

[24] Zhang K.W., A two-well structure and intrinsic mountain pass points, Cal. Var. Partial Differential Equations 13 (2001) 231-264. | MR 1861099 | Zbl 0997.49013