Bounded weak solutions of an elliptic-parabolic Neumann problem
HTML articles powered by AMS MathViewer
- by J. Hulshof PDF
- Trans. Amer. Math. Soc. 303 (1987), 211-227 Request permission
Abstract:
In this paper we establish existence and uniqueness for bounded weak solutions of an elliptic-parabolic Neumann problem. We also describe the asymptotic behavior as $t \to \infty$.References
- Hans Wilhelm Alt and Stephan Luckhaus, Quasilinear elliptic-parabolic differential equations, Math. Z. 183 (1983), no. 3, 311–341. MR 706391, DOI 10.1007/BF01176474
- M. Bertsch and J. Hulshof, Regularity results for an elliptic-parabolic free boundary problem, Trans. Amer. Math. Soc. 297 (1986), no. 1, 337–350. MR 849483, DOI 10.1090/S0002-9947-1986-0849483-0
- Emmanuele DiBenedetto and Ronald Gariepy, Local behavior of solutions of an elliptic-parabolic equation, Arch. Rational Mech. Anal. 97 (1987), no. 1, 1–17. MR 856306, DOI 10.1007/BF00279843
- C. J. van Duyn, Nonstationary filtration in partially saturated porous media: continuity of the free boundary, Arch. Rational Mech. Anal. 79 (1982), no. 3, 261–265. MR 658390, DOI 10.1007/BF00251906
- C. J. van Duyn and L. A. Peletier, Nonstationary filtration in partially saturated porous media, Arch. Rational Mech. Anal. 78 (1982), no. 2, 173–198. MR 648943, DOI 10.1007/BF00250838 J. Hulshof, An elliptic-parabolic problem: continuity of the interface, Rep. No. 10, Math. Inst. of Leiden University, 1985. J. Hulshof and L. A. Peletier, An elliptic-parabolic free boundary problem, Rep. No. 14, Math. Inst. of Leiden University, 1984. D. Kröner and J. F. Rodrigues, Global behavior for bounded solutions of a porous media equation of elliptic-parabolic type, Report, Bonn Univ., 1983. O. A. Ladyženskaja, V. A. Solonnikov and N. N. Ural’ceva, Linear and quasilinear equations of parabolic type, Transl. Math. Monographs, vol. 23, Amer. Math. Soc., Providence, R.I., 1968.
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 303 (1987), 211-227
- MSC: Primary 35M05; Secondary 35R35
- DOI: https://doi.org/10.1090/S0002-9947-1987-0896018-3
- MathSciNet review: 896018