The filtration equation in a class of functions decreasing at infinity
HTML articles powered by AMS MathViewer
- by D. Eidus and S. Kamin
- Proc. Amer. Math. Soc. 120 (1994), 825-830
- DOI: https://doi.org/10.1090/S0002-9939-1994-1169025-2
- PDF | Request permission
Abstract:
We deal with the Cauchy and external boundary problems for the nonlinear filtration equation with variable density. For each density we define a class $\phi$ of initial functions $\varphi$, such that for any $\varphi \in \phi$ the problem is uniquely solvable in some set of functions decreasing at infinity with respect to space variables.References
- Philippe Bénilan, Michael G. Crandall, and Michel Pierre, Solutions of the porous medium equation in $\textbf {R}^{N}$ under optimal conditions on initial values, Indiana Univ. Math. J. 33 (1984), no. 1, 51–87. MR 726106, DOI 10.1512/iumj.1984.33.33003
- Haïm Brezis and Shoshana Kamin, Sublinear elliptic equations in $\textbf {R}^n$, Manuscripta Math. 74 (1992), no. 1, 87–106. MR 1141779, DOI 10.1007/BF02567660
- Emmanuele DiBenedetto, Continuity of weak solutions to a general porous medium equation, Indiana Univ. Math. J. 32 (1983), no. 1, 83–118. MR 684758, DOI 10.1512/iumj.1983.32.32008
- D. Eidus, The Cauchy problem for the nonlinear filtration equation in an inhomogeneous medium, J. Differential Equations 84 (1990), no. 2, 309–318. MR 1047572, DOI 10.1016/0022-0396(90)90081-Y A. S. Kalashnikov, The Cauchy problem in a class of growing functions, Vestnik Moskov. Univ. Ser. VI, Mat. Mekh. 6 (1963), 17. (Russian)
- 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
Bibliographic Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 825-830
- MSC: Primary 35K55; Secondary 35K65, 76S05
- DOI: https://doi.org/10.1090/S0002-9939-1994-1169025-2
- MathSciNet review: 1169025