Processus associés à l'équation des milieux poreux
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 23 (1996) no. 4, pp. 793-832.
@article{ASNSP_1996_4_23_4_793_0,
     author = {Benachour, S. and Chassaing, P. and Roynette, B. and Vallois, P.},
     title = {Processus associ\'es \`a l'\'equation des milieux poreux},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {793--832},
     publisher = {Scuola normale superiore},
     volume = {4e s{\'e}rie, 23},
     number = {4},
     year = {1996},
     mrnumber = {1469575},
     zbl = {0892.60071},
     language = {fr},
     url = {http://archive.numdam.org/item/ASNSP_1996_4_23_4_793_0/}
}
TY  - JOUR
AU  - Benachour, S.
AU  - Chassaing, P.
AU  - Roynette, B.
AU  - Vallois, P.
TI  - Processus associés à l'équation des milieux poreux
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1996
SP  - 793
EP  - 832
VL  - 23
IS  - 4
PB  - Scuola normale superiore
UR  - http://archive.numdam.org/item/ASNSP_1996_4_23_4_793_0/
LA  - fr
ID  - ASNSP_1996_4_23_4_793_0
ER  - 
%0 Journal Article
%A Benachour, S.
%A Chassaing, P.
%A Roynette, B.
%A Vallois, P.
%T Processus associés à l'équation des milieux poreux
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1996
%P 793-832
%V 23
%N 4
%I Scuola normale superiore
%U http://archive.numdam.org/item/ASNSP_1996_4_23_4_793_0/
%G fr
%F ASNSP_1996_4_23_4_793_0
Benachour, S.; Chassaing, P.; Roynette, B.; Vallois, P. Processus associés à l'équation des milieux poreux. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 23 (1996) no. 4, pp. 793-832. http://archive.numdam.org/item/ASNSP_1996_4_23_4_793_0/

[A] D.J. Aronson, Regularity properties of flows through porous media, SIAM J. Appl. Math. 17 (1969), 461-467. | MR | Zbl

[AB] D.J. Aronson - P. Benilan, Régularité des solutions de l'équation des milieux poreux dans RN, C.R. Acad. Sci. Paris Sér. IA 288 (1979), 103-105. | Zbl

[B1] G.I. Barenblatt, On some unsteady motions of a liquid or a gas in a porous medium, Prikl. Mat. Mekh. 16 (1952), 67-78. | MR | Zbl

[B2] P. Benilan, A strong regularity Lp for solution of the porous media equation, Research notes Math. 89, Pitman, London, 1983. | MR | Zbl

[BC] P. Benilan - M.G. Crandal, The continuous dependence on ϕ of solutions of ut = Δϕ(u), Indiana Univ. Math. J. 30 (1981), 161-177. | Zbl

[BCP] P. Benilan - M.G. Crandal - M. Pierre, Solutions of the porous medium equation in RN under optimal conditions on initial values, Indiana Univ. Math. J. 33 (1984), 51-87. | MR | Zbl

[BM] S. Benachour - M.S. Moulay, Régularité des solutions de l'équation des milieux poreux en une dimension d'espace, C.R. Acad. Sci. Paris Sér. IA 298 (1984), 107-110. | MR | Zbl

[GM] M.E. Gurtin - R.C. Mac Camy, On the diffusion of biological populations, Math. Biosci. 33 (1977), 35-49. | MR | Zbl

[K1] A.S. Kalashnikov, Some problems of the qualitative theory of non linear degenerate second order parabolic equations, Russ. Math. Surv. 42 (1987), 169-222. | MR | Zbl

[K2] B.F. Kneer, The porous medium equation in one dimension, Trans. Amer. Math. Soc. 234 (1977), 381-415. | MR | Zbl

[KR] G. Kerkyacharian - B. Roynette, Une démonstration simple des théorèmes de Kolmogorov, Donsker et Itô Nisio, C.R. Acad. Sci. Paris Sér. IA 312 1991, 877-882. | MR | Zbl

[KS] J. Karatzas - S.E. Shreve, Brownian motion and stochastic calculus, Graduate Texts in Math., second edition, Springer Verlag, New York, 1991. | MR | Zbl

[LSU] O.A. Ladyzhenskaya - V.A. Solonnikov - N.N. Ural'Ceva, Linear and quasilinear equation of parabolic type, Translation of Mathematical monographs 23, AMS, Providence R.I., 1968. | Zbl

[M] M. Muskat, The flow of homogeneous fluids through porous media, Mc Graw-Hill, New York, 1977.

[MR] S. Meleard - ROELLY-COPPOLETTA, A propagation of chaos result for a system of particules with moderate interaction, Stochastic Process. Appli. 26 (1987), 317-332. | MR | Zbl

[OKC] O.A. Oleinik - A.S. Kalashinikov - Chzou Yui-Lin, The Cauchy problem and boundary problems for equations of the type of nonstationary filtration, Izv. Akad. Nauk. USSR Ser. Mat. 22 (1958), 667-704. | MR

[P1] R.E. Pattle, Diffusion from an instantaneous point with concentration dependent coefficent, Quart. Mech. Appl. Math. 12 (1959), 407- 409. | MR | Zbl

[P2] P. Protter, Stochastic integration and differential equations, Appl. of Math., Springer, 1990. | MR | Zbl

[RV] B. Roynette - P. Vallois, Instabilité de certaines équations différentielles stochastiques non linéaires, J. Funct. Anal. 130 (2) (1995), 477-523. | MR | Zbl

[RY] D. Revuz - M. Yor, Continuous martingales and Brownian motion, Grundl. der Math. Wiss. 293, Springer Verlag, 1991. | MR | Zbl

[SV] A.S. Sznitman - S.R.S. Varadhan, A multidimensional process involving local time, Probab. Theory Relat. Fields 71 (4) (1986), 553-579. | MR | Zbl

[WW] E.T. Whittaker - G.N. Watson, A course of modem analysis, Cambridge Univ. Press, 1990. | Zbl

[S] A.S. Sznitman, Topics in propagation of chaos, In P.L. Hennequin Editor, Ecole d'Eté de Probabilités de Saint-Flour XIX, vol. 1464, Lecture Notes in Mathematics, Springer Verlag, Berlin, Heidelberg, New York, 1989. | MR | Zbl