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Groundwater flow in a fissurised porous stratum
1. | Istituto per le Applicazioni del Calcolo "M. Picone”, Consiglio Nazionale delle Ricerche, Via dei Taurini 19, 00185 Roma |
2. | Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli “Federico II”, Via Cintia, Monte S. Angelo, I-80126 Napoli, Italy |
References:
[1] |
G. I. Barenblatt, On some unsteady motions in a liquid or a gas in a porous medium, Prikladnaja Matematika i Mechanika, 16 (1952), 67-78. |
[2] |
G. I. Barenblatt, E. A. Ingerman, H. Shvets and J. L. Vázquez, Very intense pulse in the gorundwater flow in fissurised-porous stratum, PNAS, 97 (2000), 1366-1369.
doi: 10.1073/pnas.97.4.1366. |
[3] |
M. Bertsch, R. Dal Passo and C. Nitsch, A system of degenerate parabolic nonlinear pde's: A new free boundary problem, Interfaces Free Bound, 7 (2005), 255-276. |
[4] |
K. N. Chuen, C. C. Conley and J. A. Smoller, Positively invariant regions for systems of nonlinear diffusion equations, Indiana Univ. Math. J., 26 (1977), 373-392.
doi: 10.1512/iumj.1977.26.26029. |
[5] |
R. Dal Passo, L. Giacomelli and G. Grün, A waiting time phenomena for thin film equations, Ann. Scuola Norm. Sup. Pisa (4), 30 (2001), 437-463. |
[6] |
R. Dal Passo, L. Giacomelli and G. Grün, "Waiting Time Phenomena for Degenerate Parabolic Equations - A Unifying Approach," in "Geometric Analysis and Nonlinear Partial Differential Equations" (S. Hildebrant and H. Karcher, eds.), Springer-Verlag, (2003), 637-648. |
[7] |
R. Kersner, Nonlinear heat conduction with absorption: Space localization and extinction in finite time, SIAM J. Appl. Math., 43 (1983), 1274-1285.
doi: 10.1137/0143085. |
[8] |
Y. Shvets, "Problems of Flooding in Porous and Fissured Porous Rock," Ph.D. thesis, University of California, Berkeley, 2005, http://gradworks.umi.com/31/87/3187151.html. |
[9] |
J. Simon, Compact sets in the space $L^p(0,T;B)$, Ann. Mat. Pura Appl. (4), 146 (1987), 65-96. |
[10] |
G. Stampacchia, "Équationes Elliptiques Du Second Ordre à Coefficients Discontinus," Les presses de l'université de Montréal, 1966. |
[11] |
J. L. Vázquez, "The Porous Medium Equation. Mathematical Theory," Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, Oxford, 2007. |
show all references
References:
[1] |
G. I. Barenblatt, On some unsteady motions in a liquid or a gas in a porous medium, Prikladnaja Matematika i Mechanika, 16 (1952), 67-78. |
[2] |
G. I. Barenblatt, E. A. Ingerman, H. Shvets and J. L. Vázquez, Very intense pulse in the gorundwater flow in fissurised-porous stratum, PNAS, 97 (2000), 1366-1369.
doi: 10.1073/pnas.97.4.1366. |
[3] |
M. Bertsch, R. Dal Passo and C. Nitsch, A system of degenerate parabolic nonlinear pde's: A new free boundary problem, Interfaces Free Bound, 7 (2005), 255-276. |
[4] |
K. N. Chuen, C. C. Conley and J. A. Smoller, Positively invariant regions for systems of nonlinear diffusion equations, Indiana Univ. Math. J., 26 (1977), 373-392.
doi: 10.1512/iumj.1977.26.26029. |
[5] |
R. Dal Passo, L. Giacomelli and G. Grün, A waiting time phenomena for thin film equations, Ann. Scuola Norm. Sup. Pisa (4), 30 (2001), 437-463. |
[6] |
R. Dal Passo, L. Giacomelli and G. Grün, "Waiting Time Phenomena for Degenerate Parabolic Equations - A Unifying Approach," in "Geometric Analysis and Nonlinear Partial Differential Equations" (S. Hildebrant and H. Karcher, eds.), Springer-Verlag, (2003), 637-648. |
[7] |
R. Kersner, Nonlinear heat conduction with absorption: Space localization and extinction in finite time, SIAM J. Appl. Math., 43 (1983), 1274-1285.
doi: 10.1137/0143085. |
[8] |
Y. Shvets, "Problems of Flooding in Porous and Fissured Porous Rock," Ph.D. thesis, University of California, Berkeley, 2005, http://gradworks.umi.com/31/87/3187151.html. |
[9] |
J. Simon, Compact sets in the space $L^p(0,T;B)$, Ann. Mat. Pura Appl. (4), 146 (1987), 65-96. |
[10] |
G. Stampacchia, "Équationes Elliptiques Du Second Ordre à Coefficients Discontinus," Les presses de l'université de Montréal, 1966. |
[11] |
J. L. Vázquez, "The Porous Medium Equation. Mathematical Theory," Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, Oxford, 2007. |
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