An upper bound for the waiting time for nonlinear degenerate parabolic equations. (English) Zbl 0535.35049

An upper bound is obtained for the time when the support of the solution of some nonlinear, degenerate parabolic equations begins to spread.


35K65 Degenerate parabolic equations
35K55 Nonlinear parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
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[1] Nicholas D. Alikakos, On the pointwise behavior of the solutions of the porous medium equation as \? approaches zero or infinity, Nonlinear Anal. 9 (1985), no. 10, 1095 – 1113. · Zbl 0589.35064
[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. · Zbl 0513.35079
[3] 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. · Zbl 0556.76084
[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), no. 4, 639 – 658. · Zbl 0542.76119
[5] Haïm Brézis and Michael G. Crandall, Uniqueness of solutions of the initial-value problem for \?_{\?}-\Delta \?(\?)=0, J. Math. Pures Appl. (9) 58 (1979), no. 2, 153 – 163. · Zbl 0408.35054
[6] 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. · Zbl 0425.35060
[7] Barry F. Knerr, The porous medium equation in one dimension, Trans. Amer. Math. Soc. 234 (1977), no. 2, 381 – 415. · Zbl 0365.35030
[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 the physical sciences (Bielefeld, 1979), Surveys Reference Works Math., vol. 6, Pitman, Boston, Mass.-London, 1981, pp. 229 – 241.
[10] 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. · Zbl 0101.21101
[11] 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. · Zbl 0528.76096
[12] -, The interfaces of one-dimensional flows in porous media (to appear). · Zbl 0524.35060
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