Geodesic
Decay estimates for solutions of a class of parabolic problems arising in filtration through porous media
Bollettino della Unione matematica italiana, Série 8, 4B (2001) no. 2, pp. 473-481.

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In questo lavoro si studia un problema di valori al contorno parabolico non lineare che si incontra nello studio dell'infiltrazione di un gas in un mezzo poroso. Si stabiliscono condizioni sui dati che determinano un comportamento di tipo esponenziale decrescente nel tempo per la soluzione e il suo gradiente. Si costruiscono inoltre stime esplicite. 
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Philippin, G. A.; Vernier-Piro, S. Decay estimates for solutions of a class of parabolic problems arising in filtration through porous media. Bollettino della Unione matematica italiana, Série 8, 4B (2001) no. 2, pp. 473-481. http://geodesic.mathdoc.fr/item/BUMI_2001_8_4B_2_a10/

[1] H. Amann, Quasilinear evolution equations and parabolic systems, Trans. Amer. Math. Soc., 293 (1986), 191-227. | MR | Zbl

[2] D. G. Aronson, The porous medium equation, Lecture Notes in Math., 1224 (1985), 1-46. | MR | Zbl

[3] J. M. Ball, Remarks on blow-up and nonexistence theorems for nonlinear evolution equations, Quart. J. Math. Oxford, 28 (1977), 473-486. | MR | Zbl

[4] A. Friedman, Remarks on the maximum principle for parabolic equations and its applications, Pacific J. of Math., 8 (1958), 201-211. | fulltext mini-dml | MR | Zbl

[5] H. Kielhöfer, Halbgruppen und semilineare Anfangs-randwert-probleme, Manuscripta Math., 12 (1974), 121-152. | MR | Zbl

[6] L. Nirenberg, A strong maximum principle for parabolic equations, Comm. Pure and Appl. Math., 6 (1953), 167-177. | MR | Zbl

[7] L. E. Payne-G. A. Philippin, Decay bounds for solutions of second order parabolic problems and their derivatives, Math. Models and Meth. in Appl. Sci., 5 (1995), 95-110. | MR | Zbl

[8] L. E. Payne-G. A. Philippin, Decay bounds in quasilinear parabolic problems; in Nonlinear Problems in Applied Mathematics, Ed. by T. S. Angell, L. Pamela Cook, R. E. Kleinman and W. E. Olmstead, SIAM (1996), 206-216. | Zbl

[9] G. A. Philippin-S. Vernier-Piro, Explicit exponential decay bounds, in quasilinear parabolic problems, J. of Inequalities and Applications, 3 (1999), 1-23. | MR | Zbl

[10] G. A. Philippin-S. Vernier-Piro, Explicit decay bounds in some quasilinear onedimensional parabolic problems, Math. Models and Methods in Appl. Sci., 22 (1999), 101-109. | MR | Zbl

[11] M. H. Protter-H. F. Weinberger, Maximum Principles in Differential Equations, Springer Verlag, Berlin (1984). | MR | Zbl

[12] A. E. Scheidegger, The physics of flow through porous media, Univ. of Toronto Press, Toronto (1974). | Zbl

[13] R. Sperb, Maximum principles and their applications, Academic Press Math. in Sci. and Engineering, 157 (1981). | MR | Zbl

[14] B. Straughan, Instability, Nonexistence and Weighted Energy Methods in Fluid Dynamics and Related Theories, Pitman Research Notes in Mathematics, 74 (1982). | MR | Zbl