Bulletin of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-9485(e) ISSN 0273-0979(p)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Retrieve article in: PDF

Book Information

Author(s): Panagiota Daskalopoulos and Carlos E. Kenig
Title: Degenerate diffusions
Additional book information: EMS Tracts in Mathematics 1, European Mathematical Society, Zurich, 2007, x+198 pp., ISBN 978-3-03719-033-36

References:

1.: D. G. Aronson and Ph. Bénilan, Régularité des solutions de l'équation milieux poreux dans $\mathbf{R}^{n}$ , C. R. Acad. Sci. Paris, 288(1979), 103-105. MR 524760 (82i:35090)
2.: D. G. Aronson and L. A. Caffarelli, The initial trace of a solution of the porous medium equation, Trans. Amer. Math. Soc., 280(1983), 351-366. MR 712265 (85c:35042)
3.: G. I. Barenblatt, On some unsteady motions of a liquid or a gas in a porous medium, Prikl. Mat. Mekh., 16(1952), 67-78 (in Russian). MR 0046217 (13:700a)
4.: P. Bénilan, M. G. Crandall and M. Pierre, Solutions of the porous medium equation in $\mathbf{R}^{n}$ under optimal conditions on the initial values, Indiana Univ. Math. J., 33(1984), 51-87. MR 726106 (86b:35084)
5.: J. Boussinesq, Recherches théoriques sur l'écoulement des nappes d'eau infiltrés dans le sol et sur le débit de sources, C. R. Acad. Sci./J. Math. Pures Appl., 10(1903/04), 5-78.
6.: B. E. Dahlberg and C. E. Kenig, Non-negative solutions of the porous medium equation, Comm. Partial Differential Equations, 9(1984), 409-437. MR 741215 (85j:35099)
7.: E. DiBenedetto, Degenerate Parabolic Equations, Springer Verlag, New York, 1993. MR 1230384 (94h:35130)
8.: M. A. Herrero and M. Pierre, The Cauchy problem for $u_{t}=\Delta u^{m}$ when , Trans. Amer. Math. Soc., 291(1985), 145-158. MR 797051 (86i:35065)
9.: L. S. Leibenzon, The motion of a gas in a porous medium, Complete Works, Vol. 2, Acad. Sci. URSS, Moscow 1930 (in Russian).
10.: M. Muskat, The Flow of Homogeneous Fluids Through Porous Media, McGraw-Hill, New York, 1937.
11.: M. Pierre, Uniqueness of the solution of $u_{t}-\Delta \varphi (u)=0$ with initial datum a measure, Nonlinear Anal., 6 (1982), 175-187. MR 651699 (83h:35062)
12.: P. Sacks, Continuity of solutions of a singular parabolic equation, Nonlinear Anal., 7(1983), 387-409. MR 696738 (84d:35081)
13.: Juan Luis Vazquez, Smoothing and Decay Estimates for Nonlinear Diffusion Equations, Oxford Lecture Series in Mathematics and Its Applications, Oxford University Press, Oxford, 2006. MR 2282669 (2007k:35008)
14.: Juan Luis Vazquez, The Porous Medium Equation. Mathematical theory, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, Oxford, 2007. MR 2286292 (2008e:35003)
15.: D. V. Widder, Positive temperature on a infinite rod, Trans. Amer Math. Soc., 55(1944), 85-95. MR 0009795 (5:203f)

Additional Information:

Reviewer(s):
D. G. Aronson
Affiliation: School of Mathematics and Institute for Mathematics and Its Applications University of Minnesota
Email: don@ima.umn.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 47 (2010), 171-176.

MSC (2000): Primary 35-02, 35K55, 35K65
DOI: 10.1090/S0273-0979-09-01272-5
PII: S 0273-0979(09)01272-5
Posted: July 21, 2009
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|