An upper bound for the waiting time for nonlinear degenerate parabolic equations
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- by Michel Chipot and Thomas Sideris
- Trans. Amer. Math. Soc. 288 (1985), 423-427
- DOI: https://doi.org/10.1090/S0002-9947-1985-0773069-9
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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.References
- Nicholas D. Alikakos, On the pointwise behavior of the solutions of the porous medium equation as $t$ approaches zero or infinity, Nonlinear Anal. 9 (1985), no. 10, 1095–1113. MR 806912, DOI 10.1016/0362-546X(85)90088-4 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.
- D. G. Aronson and L. A. Caffarelli, The initial trace of a solution of the porous medium equation, Trans. Amer. Math. Soc. 280 (1983), no. 1, 351–366. MR 712265, DOI 10.1090/S0002-9947-1983-0712265-1
- 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), no. 4, 639–658. MR 704481, DOI 10.1137/0514049
- Haïm Brézis and Michael G. Crandall, Uniqueness of solutions of the initial-value problem for $u_{t}-\Delta \varphi (u)=0$, J. Math. Pures Appl. (9) 58 (1979), no. 2, 153–163. MR 539218
- Luis A. Caffarelli and Avner Friedman, Continuity of the density of a gas flow in a porous medium, Trans. Amer. Math. Soc. 252 (1979), 99–113. MR 534112, DOI 10.1090/S0002-9947-1979-0534112-2
- Barry F. Knerr, The porous medium equation in one dimension, Trans. Amer. Math. Soc. 234 (1977), no. 2, 381–415. MR 492856, DOI 10.1090/S0002-9947-1977-0492856-3 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.
- L. A. Peletier, The porous media equation, Applications of nonlinear analysis in the physical sciences (Bielefeld, 1979), Surveys Reference Works Math., vol. 6, Pitman, Boston, Mass.-London, 1981, pp. 229–241. MR 659697
- E. S. Sabinina, On the Cauchy problem for the equation of nonstationary gas filtration in several space variables, Soviet Math. Dokl. 2 (1961), 166–169. MR 0158190
- Juan Luis Vázquez, Asymptotic behaviour and propagation properties of the one-dimensional flow of gas in a porous medium, Trans. Amer. Math. Soc. 277 (1983), no. 2, 507–527. MR 694373, DOI 10.1090/S0002-9947-1983-0694373-7 —, The interfaces of one-dimensional flows in porous media (to appear).
Bibliographic Information
- © Copyright 1985 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 288 (1985), 423-427
- MSC: Primary 35K65; Secondary 35B45, 35K55
- DOI: https://doi.org/10.1090/S0002-9947-1985-0773069-9
- MathSciNet review: 773069