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Transactions of the American Mathematical Society

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An upper bound for the waiting time for nonlinear degenerate parabolic equations

Authors: Michel Chipot and Thomas Sideris
Journal: Trans. Amer. Math. Soc. 288 (1985), 423-427
MSC: Primary 35K65; Secondary 35B45, 35K55
MathSciNet review: 773069
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Abstract: An upper bound is obtained for the time when the support of the solution of some nonlinear, degenerate parabolic equations begins to spread.

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  • [1] N. D. Alikakos, On the pointwise behavior of the solutions of the porous medium equation as $ t$ approaches zero or infinity (to appear). MR 806912 (87a:35108)
  • [2] D. G. Aronson, Some properties of the interface for gas flow in porous media, Proceedings of the Montecatini Symposium on Free Boundary Problems, Pitman, New York, 1983.
  • [3] D. G. Aronson and L. A. Caffarelli, The initial trace of a solution of the porous medium equations (to appear). MR 712265 (85c:35042)
  • [4] D. G. Aronson, L. A. Caffarelli and S. Kamin, How an initially stationary interface begins to move in porous medium flow, SIAM J. Math. Anal. 14 (1983), 639-658. MR 704481 (84g:35084)
  • [5] H. Brezis and M. G. Crandall, Uniqueness of solution of the initial-value problem for $ {u_t} - \Delta \phi (u) = 0$, J. Math. Pures Appl. (9) 58 (1979), 153-163. MR 539218 (80e:35029)
  • [6] L. A. Caffarelli and A. Friedman, Continuity of the density of a gas flow in a porous medium, Trans. Amer. Math. Soc. 252 (1979), 99-111. MR 534112 (80i:35090)
  • [7] B. F. Knerr, The porous medium equation in one dimension, Trans. Amer. Math. Soc. 234 (1977) 381-415. MR 0492856 (58:11917)
  • [8] O. A. Oleinik, A. S. Kalasnikov and Yui-lin'Czou, The Cauchy problem and boundary problems for equations of the type of nonstationary filtration, Izv. Akad. Nauk SSSR Ser. Mat. 22 (1958), 607-704.
  • [9] L. A. Peletier, The porous media equation, Applications of Nonlinear Analysis in Physical Sciences (Proceedings of a meeting held at Bielefeld, W. Germany, 1979), Pitman, New York, 1981. MR 659697 (83k:76076)
  • [10] E. S. Sabinina, On the Cauchy problem for the equations of nonstationary gas filtration in several space variables, Dokl. Akad. Nauk SSSR 136 (1961), 1034-1037. MR 0158190 (28:1416)
  • [11] J. L. Vazquez, Asymptotic behaviour and propagation properties of the one-dimensional flow of gas in a porous medium, Trans. Amer. Math. Soc. 277 (1983), 506-527. MR 694373 (84h:35014)
  • [12] -, The interfaces of one-dimensional flows in porous media (to appear).

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Keywords: Nonlinear degenerate parabolic equations, waiting time
Article copyright: © Copyright 1985 American Mathematical Society

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