Stefan problems with nonlinear diffusion and convection

Journal of Differential Equations

Volumn 210, Issue 2, 2005, Pages 383-428

  Blanchard, D ^a,b   Porretta, A ^c  

^a UNIVERSITÉ DE ROUEN   (France)

^b UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

^c UNIVERSITY OF ROME TOR VERGATA   (Italy)

Author keywords

Integrable data; L1 contraction principle; Nonlinear Stefan problems with convection; Renormalized solutions

Indexed keywords

EID: 13844255285     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jde.2004.06.012     Document Type: Article

References (21)

1. H. Alt S. Luckhaus Quasilinear elliptic-parabolic differential equations Math. Z. 183 3 1983 311-341
2. P. Bénilan Equations d'evolution dans un espace de Banach quelconque et applications 1972 These d'Etat Orsay
3. A. Ben Cheick O. Guibé Resultats d'existence et d'unicité pour une classe de problemes non lineaires et non coercifs C.R. Acad. Sci. Paris Ser. I Math. 329 11 1999 967-972
4. D. Blanchard G. Francfort A few results on a class of degenerate parabolic equations Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 18 1991 213-249
5. 1data: Existence and uniqueness Proc. Roy. Soc. Edinburgh Sect. A 127 1997 1137-1152
6. D. Blanchard A. Porretta Nonlinear parabolic equations with natural growth terms and measure initial data Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 30 3-4 2001 583-622
7. D. Blanchard H. Redwane Renormalized solutions for a class of nonlinear evolution problems J. Math. Pures Appl. 77 1998 117-151
8. t - Δφ(u) = 0 J. Math. Pures. Appl. 58 1979 153-163
9. J. Carrillo Entropy solutions for nonlinear degenerate problems Arch. Rat. Mech. Anal. 147 1999 269-361
10. J. Carrillo P. Wittbold Uniqueness of renormalized solutions of degenerate elliptic-parabolic problems J. Differential Equations 156 1 1999 93-121
11. G. Dal Maso F. Murat L. Orsina A. Prignet Renormalized solutions of elliptic equations with general measure data Ann. Scuola Norm. Sup. Pisa Cl. Sci. 28 4 1999 741-808
12. A. Damlamian Some result on the multiphase Stefan problem Comm. Partial Diff. Equations 2 1977 1017-1044
13. R.J. Di Perna P.L. Lions On the Cauchy problem for Boltzmann equations: global existence and weak stability Ann. of Math. 130 1989 321-366
14. A. Friedman Variational Principles and Free-boundary Problems 1982 Wiley New York
15. N. Igbida M. Urbano Uniqueness for nonlinear degenerate problems NoDea Nonlinear Differential Equation Appl. 30 2003 287-307
16. N. Igbida, P. Wittbold, Renormalized solution for Stefan type problems: existence and uniqueness, in preparation.
17. S.N. Kružkov First order quasilinear equations with several independent variables Mat. Sb. (N.S.) 81 123 1970 228-255
18. R. Landes On the existence of weak solutions for quasilinear parabolic boundary value problems Proc. Roy. Soc. Edinburgh Sect. A 89 1981 217-237
19. 1-contraction and uniqueness for quasilinear elliptic-parabolic equations J. Differential Equations 131 1996 20-38
20. A. Porretta Existence results for nonlinear parabolic equations via strong convergence of truncations Ann. Mat. Pura Appl. (IV) 177 1999 143-172
21. D. Tarzia, A bibliography on moving-free boundary problems for the heat-diffusion equation. The Stefan and related problems, M.A.T. Seria A: Mathematical Conferences, Seminar and Papers, Vol. 2, 2000.