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Self-similar focusing in porous media: An explicit calculation
1. | Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN 55455, United States |
References:
[1] |
S. B. Angenent and D. G. Aronson, The focussing problem for the radially symmetric porous medium equation, Comm. PDE, 20 (1995), 1217-1240.
doi: 10.1080/03605309508821130. |
[2] |
S. B. Angenent and D. G. Aronson, Self-similarity in the post-focussing regime in porous medium flows, Euro. J. Appl. Math., 7 (1996), 277-285. |
[3] |
D. G. Aronson, The porous medium equation, in "Nonlinear Diffusion Problems" (Montecatini Terme, 1985), Lecture Notes in Mathematics, 1224, Springer, Berlin, (1986), 1-46. |
[4] |
D. G. Aronson and J. Graveleau, A self-similar solution to the focusing problem for the porous medium equation, Euro. J. Appl. Math., 4 (1993), 65-81. |
[5] |
G. I. Barenblatt, "Scaling, Self-Similarity, and Intermediate Asymptotics," With a foreword by Ya. B. Zeldovich, Cambridge Texts in Applied Mathematics, 14, Cambridge University Press, Cambridge, 1996. |
[6] |
G. I. Barenblatt, On some unsteady motions of a liquid or gas in a porous medium, Akad. Nauk SSSR Prikl. Mat. Meh., 16 (1952), 67-78. |
[7] |
Ph. Bénilan, M. G. Crandall and M. Pierre, Solutions of the porous medium equation in $\mathbfR^N$ under optimal conditions on initial values, Indiana U. Math. J., 33 (1984), 51-87.
doi: 10.1512/iumj.1984.33.33003. |
[8] |
B. E. J. Dahlberg and C. E. Kenig, Nonnegative solutions of the porous medium equation, Comm. PDE, 9 (1984), 409-437. |
show all references
References:
[1] |
S. B. Angenent and D. G. Aronson, The focussing problem for the radially symmetric porous medium equation, Comm. PDE, 20 (1995), 1217-1240.
doi: 10.1080/03605309508821130. |
[2] |
S. B. Angenent and D. G. Aronson, Self-similarity in the post-focussing regime in porous medium flows, Euro. J. Appl. Math., 7 (1996), 277-285. |
[3] |
D. G. Aronson, The porous medium equation, in "Nonlinear Diffusion Problems" (Montecatini Terme, 1985), Lecture Notes in Mathematics, 1224, Springer, Berlin, (1986), 1-46. |
[4] |
D. G. Aronson and J. Graveleau, A self-similar solution to the focusing problem for the porous medium equation, Euro. J. Appl. Math., 4 (1993), 65-81. |
[5] |
G. I. Barenblatt, "Scaling, Self-Similarity, and Intermediate Asymptotics," With a foreword by Ya. B. Zeldovich, Cambridge Texts in Applied Mathematics, 14, Cambridge University Press, Cambridge, 1996. |
[6] |
G. I. Barenblatt, On some unsteady motions of a liquid or gas in a porous medium, Akad. Nauk SSSR Prikl. Mat. Meh., 16 (1952), 67-78. |
[7] |
Ph. Bénilan, M. G. Crandall and M. Pierre, Solutions of the porous medium equation in $\mathbfR^N$ under optimal conditions on initial values, Indiana U. Math. J., 33 (1984), 51-87.
doi: 10.1512/iumj.1984.33.33003. |
[8] |
B. E. J. Dahlberg and C. E. Kenig, Nonnegative solutions of the porous medium equation, Comm. PDE, 9 (1984), 409-437. |
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