Global solutions to viscous Hamilton-Jacobi equations with irregular initial data

Communications in Partial Differential Equations

Volumn 24, Issue 11-12, 1999, Pages 1999-2021

  Benachour, Said ^a   Laurençot, Philippe ^a  

^a UNIVERSITÉ HENRI POINCARÉ NANCY 1   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033475432     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1080/03605309908821492     Document Type: Article

References (19)

1. N. Alaa, Solutions faibles d'équations paraboliques quasilinéaires avec données initiales mesures, Ann. Math. Blaise Pascal 3 (1996), 1-16.
2. L. Amour and M. Ben-Artzi. Global existence and decay for viscous Hamilton-Jacobi equations, Nonlinear Anal. 31 (1998), 621-628.
3. M. Ben-Artzi, Global existence and decay for a nonlinear parabolic equation, Nonlinear Anal. 19 (1992), 763-768.
4. M. Ben-Artzi, J. Goodman and A. Levy, Remarks on a nonlinear parabolic equation. Trans. Amer. Math. Soc., to appear.
5. M. Ben-Artzi and H. Koch. Decay of mass for a semilinear parabolic equation. Comm. Partial Differential Equations, to appear.
6. S. Benachour and Ph. Laurençot, Very singular solutions to a nonlinear parabolic equation with absorption. I. Existence, preprint WIAS 468, 1999.
7. t - Δu + |∇u| = 0, manuscript.
8. x|, Astérisque 236 (1996), 41-71.
9. d, d ≥ 2, J. Funct. Anal. 144 (1997), 301-324.
10. Ph. Bénilan, Evolution equations and accretive operators, Lecture notes taken by S. Lenhardt, Univ. of Kentucky, Spring 1981.
11. L. Boccardo, F. Murat and J.P. Puel, Existence results for some quasilinear parabolic equations, Nonlinear Anal. 13 (1988), 373-392.
12. S. Bonafede and D. Schmitt, "Triangular" reaction-diffusion systems with integiable initial data, Nonlinear Anal. 33 (1998), 785-801.
13. H. Brezis and T. Cazenave, Nonlinear evolution equations, in preparation.
14. H. Brezis and A. Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pures Appl. 62 (1983), 73-97.
15. O. Kavian, Introduction à la théorie des points critiques et applications aux problèmes elliptiques, Math. Appl. 13, SMAI, Springer-Verlag, Paris, 1993.
16. O.A. Ladyženskaja, V.A. Solonnikov and N.N. Ural'ceva, Linear and quasilinear equations of parabolic type, Transl. Math. Monogr. 23, Amer. Math. Soc., Providence, 1968.
17. P.L. Lions, Generalized solutions of Hamilton-Jacobi equations, Pitman Res. Notes Math. Ser. 69, Longman, Harlow, 1982.
18. p'(0, T; B), Ann. Mat. Pura Appl. (4) 146 (1987). 65-96.
19. Ph. Souplet and F.B. Weissler, Poincaré inequality and global solutions of a nonlinear parabolic equation, Ann. Inst. H. Poincaré Anal. Non Linéaire, to appear.