L1-contraction and uniqueness for quasilinear elliptic-parabolic equations

Journal of Differential Equations

Volumn 131, Issue 1, 1996, Pages 20-38

  Otto, Felix ^a  

^a UNIVERSITY OF BONN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030579044     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1996.0155     Document Type: Article

References (24)

1. H. W. Alt and S. Luckhaus, Quasilinear elliptic-parabolic differential equations, Math. Z. 183 (1983), 311-341.
2. H. W. Alt, S. Luckhaus, and A. Visintin, On nonstationary flow through porous media, Ann. Mat. Pura Appl. 136 (1984), 303-316.
3. Y. Amirat, Écoulements en milieu poreux n'obéissant pas à la loi de Darcy, RAIRO, Modél. Math. Anal. Numér. 25, No. 3 (1991), 273-306.
4. t - Δφ(u) = 0, J. Math. Pures Appl. 58 (1979), 153-163.
5. J. Carrillo, On the uniqueness of the solution of the evolution dam problem, Nonlinear Anal. 22, No. 5 (1994), 573-607.
6. M. G. Crandall and P.-L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 277 (1983), 1-42.
7. C. J. van Duijn and P. Knabner, Solute transport in porous media with equilibrium and non-equilibrium multiple-site adsorption: Travelling waves, J. Reine Angew. Math. 415 (1991), 1-49.
8. B. H. Gilding, A nonlinear degenerate parabolic equation, Ann. Scuola Norm. Sup. Pisa Cl. Sci. VI 4, No. 3 (1977), 393-432.
9. G. Gagneux and M. Madaune-Tort, Unicité des solutions faibles d'équations de diffusion- convection, C. R. Acad. Sc. Paris Sér. I Math. 318 (1994), 919-924.
10. B. H. Gilding and L. A. Peletier, The Cauchy problem for an equation in the theory of infiltration, Arch. Rational Mech. Anal. 61, No. 2 (1976), 127-140.
11. S. Kamin, Source-type solutions for equations of nonstationary filtration, J. Math. Anal. Appl. 64 (1978), 263-276.
12. A. S. Kalashnikov, Some problems of the qualitative theory of non-linear degenerate second-order parabolic equations, Russian Math. Surveys 42, No. 2 (1987), 169-222.
13. S. N. Kružkov, First order quasilinear equations in several independent variables, Math. USSR-Sb 10 (1970), 217-243.
14. P. Knabner and F. Otto, Solute transport in porous media with equilibrium and non- equilibrium multiple-site adsorption: Uniqueness of weak solutions, Nonlinear Anal., submitted.
15. F. Otto, in "Proceedings Conference on Free Boundary Value Problems, Oberwolfach, Germany, July 1994."
16. 1-contraction and uniqueness for quasilinear elliptic-parabolic equations, Preprint Sonderforschungsbereich 256, University of Bonn, 1995.
17. 1-contraction and uniqueness for quasilinear elliptic-parabolic equations, C. R. Acad. Sci. Paris Sér. I Math. 321 (1995), 1005-1010.
18. 1-contraction and uniqueness for unstationary saturated-unsaturated porous media flow, Adv. Math. Sci. Math., to appear.
19. A. de Pablo and J. L. Vazquez, Travelling waves and finite propagation in a reaction- diffusion equation, J. Differential Equations 93 (1991), 19-61.
20. L. A. Peletier and Z. Junning, Large time behaviour of solutions of the porous media equation with absorption: The fast diffusion case, Nonlinear Anal. 17, No. 10 (1991), 991-1009.
21. 1(Ω), Publ. Math. Fac. Sci. Besançon, Anal. Nonlinéaire 7 (1983), see also Math. Rev. 86b:35080
22. M. Tsutsumi, On solutions of some doubly nonlinear degenerate parabolic equations with absorption, J. Math. Anal. Appl. 132 (1988), 187-212.
23. A. I. Vol'pert and S. I. Hudjaev, Cauchy's problem for degenerate secon order quasi-linear parabolic equations, Math. USSR-Sb 7 (1969), 365-387.
24. J. Yin, On the uniqueness and stability of BV solutions for nonlinear diffusion equations, Comm. Partial Differential Equations 15, No. 12 (1990), 1671-1683.