Long-time behaviour for diffusion equations with fast convection

Annali di Matematica Pura ed Applicata

Volumn 175, Issue 1, 1998, Pages 233-251

  Laurenot, P H ^a  

^a UNIVERSITÉ HENRI POINCARÉ NANCY 1   (France)

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EID: 24244443280     PISSN: 03733114     EISSN: 16181891     Source Type: Journal    
DOI: 10.1007/bf01783685     Document Type: Article

References (19)

1. x + v, G. R. Acad. Sci. Paris Sér. l Math., 299 (1984), pp. 919-922.
2. 1 Ann. Inst. H. Poincaré Anal. Non Linéaire, 12 (1995), pp. 727-761.
3. A. CARPIO, Unicité et comportement asymptotiqiie pour des équations de convection-diffusion scalaires, G. R. Acad. Sci. Paris Sér. I Math., 319 (1994), pp. 51-56.
4. J. I. DIAZ - R. KERSNER, Non existence d'une des frontières libres dans une équation dé générée en théorie de la filtration, G. R. Acad. Sci. Paris Sér. I Math., 296 (1983), pp. 505-508.
5. J. I. DIAZ - R. KERSNER, On a nonlinear degenerate parabolic equation in infiltration or evaporation through a porous medium, J. Diff. Eq., 69 (1987), pp. 368-403.
6. N. DUNFORD - J. T. ScmvARTZ, Linear operators. Part I : general theory, Interscience Publishers, Inc., New York (1958).
7. M. ESCOBEDO - J. L. VAZQUEZ - E. ZUAZUA, Asymptotic behaviour and source-type solutions for a diffusion-convection equation, Arch. Rational Mech. Anal., 124 (1993), pp. 43-65.
8. M. ESCOBEDO - J. L. VAZQUEZ - E. ZUAZUA, A diffusion-convection equation in several space dimensions, Indiana Univ. Math. J., 42 (1993), pp. 1413-1440.
9. M. ESCOBEDO - E. ZUAZUA, Large time behaviour for convection-diffusion equations in R", J. Funct. Anal., 100 (1991), pp. 119-161.
10. B. H. GILDING, A nonlinear degenerate parabolic equation, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 4 (1977), pp. 393-432.
11. B. H. GILDING, The occurrence of interfaces in nonlinear diffusion-advection processes, Arch. Rational Mech. Anal., 100 (1988), pp. 243-263.
12. B. H. GILDING, Improved theory for a nonlinear degenerate parabolic equation, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 16 (1989), pp. 165-24.
13. B. H. GILDING - L. A. PELETIER, The Cauchy problem for an equation in the theory ofinfil- tration, Arch. Rational Mech. Anal., 61 (1976), pp. 127-140.
14. S. N. KRUZHKOV, Results concerning the nature of the continuity of solutions of parabolic equations and some of their applications, Math. Notes, 6 (1969), pp. 517-523.
15. S. N. KRUZHKOV - F. HILDEBRAND, The Cauchy problem for first-order quasilinear equations luhen the domain of dependence on the initial data is infinite, Moscow Univ. Math. Bull, 29 (1974), pp. 75-81.
16. PH. LAURENçOT - F. SIMONDON, Long-time behaviour for porous medium equations with. convection, Proc. Roy. Soc. Edinburgh Sect. A, 128 (1998), pp. 315-336.
17. T. P. Liu - M. PIERRE, Source-solutions and asymptotic behavior in conservation laws, J. Diff. Eq., 51 (1984), pp. 419-141.
18. S. I. SHMAREV, On a degenerate parabolic equation in filtration theory: monotonicity and C-regularity of interface, Adv. Math. Sci. Appl., 5 (1995), pp. 1-29.
19. J. SIMON, Compact sets in the space Lp(0, T; B), Ann. Mat. Pura Appl. (4), 146 (1987), pp. 65-96.