Very singular solutions to a nonlinear parabolic equation with absorption II. Uniqueness

Royal Society of Edinburgh - Proceedings A

Volumn 134, Issue 1, 2004, Pages 39-54

  Benachour, Saïd ^a   Koch, Herbert ^b   Laurençot, Philippe ^c  

^a UNIVERSITÉ HENRI POINCARÉ NANCY 1   (France)

^b TU DORTMUND UNIVERSITY   (Germany)

^c INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1942443880     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0308210500003061     Document Type: Conference Paper

References (19)

1. S. Benachour and Ph. Laurençot. Global solutions to viscous Hamilton-Jacobi equations with irregular initial data. Commun. PDEs 24 (1999), 1999-2021.
2. S. Benachour and Ph. Laurençot. Very singular solutions to a nonlinear parabolic equation with absorption. I. Existence. Proc. R. Soc. Edinb. A 131 (2001), 27-44.
3. H. Brezis and A. Friedman. Nonlinear parabolic equations involving measures as initial conditions. J. Math. Pures Appl. 62 (1983), 73-97.
4. H. Brezis, L. A. Peletier and D. Terman. A very singular solution of the heat equation with absorption. Arch. Ration. Mech. Analysis 95 (1986), 185-209.
5. M. G. Grandall, P. L. Lions and P. E. Souganidis. Maximal solutions and universal bounds for some partial differential equations of evolution. Arch. Ration. Mech. Analysis 105 (1989), 163-190.
6. J. I. Diaz and J. E. Saa. Uniqueness of very singular self-similar solution of a quasilinear degenerate parabolic equation with absorption. Publ. Mat. 36 (1992), 19-38.
7. Z. Junning. Source-type solutions of a quasilinear degenerate parabolic equation with absorption. Chin. Ann. Math. 15 (1994), 89-104.
8. S. Kamin and J. L. Vázquez. Singular solutions of some nonlinear parabolic equations. J. Analyse Math. 59 (1992), 51-74.
9. S. Kamin and L. Véron. Existence and uniqueness of the very singular solution of the porous media equation with absorption. J. Analyse Math. 51 (1988), 245-258.
10. O. A. Ladyženskaja, V. A. Solonnikov and N. N. Ural'ceva. Linear and quasilinear equations of parabolic type. Translations of Mathematical Monographs, vol. 23 (Providence, RI: American Mathematical Society, 1968).
11. p when 0 < m < 1. J. Diff. Eqns 132 (1996), 353-376.
12. G. Leoni. On very singular self-similar solutions for the porous media equation with absorption. Diff. Integ. Eqns 10 (1997), 1123-1140.
13. M. Marcus and L. Véron. Initial trace of positive solutions of some nonlinear parabolic equations. Commun. PDEs 24 (1999), 1445-1499.
14. L. Oswald. Isolated positive singularities for a nonlinear heat equation. Houston J. Math. 14 (1988), 543-572.
15. L. A. Peletier and Z. Junning. Source-type solutions of the porous media equation with absorption: the fast diffusion case. Nonlin, Analysis 14 (1990), 107-121.
16. L. A. Peletier and D. Terman. A very singular solution of the porous media equation with absorption. J. Diff. Eqns 65 (1986), 396-410.
17. L. A. Peletier and J. Wang. A very singular solution of a quasilinear degenerate diffusion equation with absorption. Trans. Am. Math. Soc. 307 (1988), 813-826.
18. Y. Qi and M. Wang. The self-similar profiles of generalized KPZ equation. Pac. J. Math. 201 (2001), 223-240.
19. J. L. Vázquez. Asymptotic behaviour of nonlinear parabolic equations. Anomalous exponents. In Degenerate diffusions (ed. W. M. Ni, L. A. Peletier and J. L. Vázquez). IMA Volumes in Mathematics and its Applications, vol. 47, pp. 215-228 (Springer, 1993).