A few results on a class of degenerate parabolic equations

 Access to full text

 Full (PDF)

1. [1] H.W. Alt - S. Luckhaus, Quasilinear Elliptic-Parabolic Differential Equations, Math. Z., 183 (1983), pp. 311-341. Zbl0497.35049MR706391
2. [2] A. Bamberger, Etude d'une équation doublement non linéaire, J. Funct. Anal., 24 (1977), pp. 148-155. Zbl0345.35059MR470490
3. [3] V. Barbu, Nonlinear Semi-Groups and Differential Equations in Banach Spaces, Noordhoff, Leiden, 1976. Zbl0328.47035MR390843
4. [4] PH. Benilan, Private communication. 
5. [5] D. Blanchard - G. Francfort, Study of a Doubly Nonlinear Heat Equation with no Growth Assumptions on the Parabolic Term, SIAM J. Math. Anal., 19 (1988), pp. 1032-1056, and Erratum, SIAM J. Math. Anal., 20 (1989), pp. 761-762. Zbl0685.35052MR957665
6. [6] L. Boccardo - T. Gallouet, On Some Nonlinear Elliptic and Parabolic Equations Involving Measure Data, J. Funct. Anal., 87 (1989), pp. 149-169. Zbl0707.35060MR1025884
7. [7] L. Boccardo - F. Murat, Remarques sur l'homogénéisation de certains problèmes quasilinéaires, Portugal. Math.41 (1982), pp. 535-562. Zbl0524.35042MR766874
8. [8] H. Brezis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North Holland, Amsterdam, 1973. Zbl0252.47055MR348562
9. [9] H. Brezis - F. Browder, Some Properties of Higher Order Sobolev Spaces, J. Math. Pures Appl.61 (1982), pp. 207-218. Zbl0512.46034MR690395
10. [10] M. Fremond, Matériaux à mémoire de forme, C. R. Acad. Sci. Paris, Sér. II, 305 (1987), pp. 741-746. 
11. [11] M. Fremond, Internal constraints and constitutive laws, Mathematical Models for Phase Change Problems, International Series of Numerical Mathematics, 88 (1989), Birkhäuser, Basel, pp. 3-18. Zbl0677.73005MR1038062
12. [12] O. Grange - F. Mignot, Sur la résolution d'une équation et d'une inéquation paraboliques non linéaires, J. Funct. Anal., 11 (1972), pp. 77-92. Zbl0251.35055MR350207
13. [13] J.L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires, Dunod, Gauthier-Villars, Paris, 1969. Zbl0189.40603MR259693
14. [14] M. Marcus - V.J. Mizel, Nemitsky Operators on Sobolev Spaces, Arch. Rational Mech. Anal., 51 (1973), pp. 347-370. Zbl0266.46029MR348480
15. [15] G. Milton - M.E. Fisher, Continuum Fluids with a Discontinuity in the Pressure, J. Statist. Phys., 32 (1983), pp. 413-438. MR715034
16. [16] G. Milton - M.E. Fisher, Classifying First-Order Phase Transitions, Physica138A (1986), pp. 22-54. MR865235
17. [17] J.J. Moreau, Fonctionnelles convexes, Cours du Collège de France, Paris, 1966. 
18. [18] F. Murat, Private communication. 
19. [19] P.A. Raviart, Sur la résolution de certaines équations paraboliques nonlinéaires, J. Funct. Anal., 5 (1970), pp. 299-328. Zbl0199.42401MR257585
20. [20] J. Simon, Compact set in Lp(0,T;B), Ann. Mat. Pura Appl. (4), 146 (1987), pp. 65-96. Zbl0629.46031MR916688
21. [21] G. Stampacchia, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier, Grenoble, 15 (1965), pp. 189-258. Zbl0151.15401MR192177
22. [22] J.L. Webb, Boundary Value Problems for Strongly Nonlinear Elliptic Equations, J. London, Math. Soc., 21 (1980), pp. 123-132. Zbl0438.35029MR576188

1. Viorel Barbu, Angelo Favini, Existence for implicit differential equations in Banach spaces
2. Nesrine Fterich, Global solution to a generalized nonisothermal Ginzburg-Landau system
3. Augusto Visintin, Structural Stability of Doubly-Nonlinear Flows