@article{M2AN_1979__13_4_297_0,
author = {Berger, Alan E. and Brezis, Ha\"\i m and Rogers, Jo\"el C. W.},
title = {A numerical method for solving the problem $u\_t - \Delta f (u) = 0$},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {13},
year = {1979},
pages = {297-312},
mrnumber = {555381},
zbl = {0426.65052},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_1979__13_4_297_0}
}
Berger, Alan E.; Brezis, Haim; Rogers, Joël C. W. A numerical method for solving the problem $u_t - \Delta f (u) = 0$. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 13 (1979) pp. 297-312. http://gdmltest.u-ga.fr/item/M2AN_1979__13_4_297_0/
1. , Regularity Properties of Flows through Porous Media, S.I.A.M., J. Appl. Math., Vol. 17, 1969, pp. 461-467. | MR 247303 | Zbl 0187.03401
2. , A finite Difference Scheme for Melting Problems, J. Inst. Math. Appl., Vol. 13, 1974, pp. 353-366. | MR 351295
3. and , Convergence of Approximations to Nonlinear Semigroups, École Polytechnique Internal Report Number 24, December 1977.
4. , Equations d'évolution dans un espace de Banach quelconque et applications, Thèse, Publications Mathématiques d'Orsay, n° 25, 1972.
5. , The Truncation Method for the Solution of a Class of Variational Inequalities, R.A.I.R.O., Analyse Numérique, Vol. 10, 1976, pp. 29-42. | Numdam | MR 455489 | Zbl 0334.49012
6. , and , Numerical Solution of a Diffusion Consumption Problem with a Free Boundary, S.I.A.M. J. Numer. Anal., Vol. 12, 1975, pp. 646-672. | MR 383779 | Zbl 0317.65032
7. , and , Numerical Solution of a Stefan Problem by a Technique of Alternating Phase Truncation, Séminaires IRIA, Analyse et contrôle des systèmes, Rocquencourt, Institut de Recherche d'Informatique et d'automatique, 1976, pp. 21-34.
8. and , An Error Estimate for the Truncation Method for the Solution of Parabolic Obstacle Variational Inequalities, Math. Comp., Vol. 31, 1977 pp. 619-628. | MR 438707 | Zbl 0367.65056
9. , On Some Degenerate Nonlinear Parabolic Equations, Nonlinear Functional Analysis, F. BROWDER, Ed., Proc. Symp. in pure math., Vol. 18, A.M.S., 1970, pp. 28-38. | MR 273468 | Zbl 0231.47034
10. and , Convergence and Approximation of Semigroups of Nonlinear Operators in Banach Spaces, J. Func. Anal., Vol. 9, 1972, pp. 63-74. | MR 293452 | Zbl 0231.47036
11. and , Semi-linear second-order elliptic equations in , J. Math. Soc. Japan, Vol. 25, 1973, pp. 565-590. | MR 336050 | Zbl 0278.35041
12. , An Introduction to Evolution Governed by Accretive Operators, Dynamical systems vol. 1, Proc. of the Int. Symp. on Dyn. Sys. at Brown U. August 12-16, 1974, L. CESARI, J. K. HALE and J. P. LASALLE, Eds, New York, Academic Press, 1976, pp. 131-165. | MR 636953 | Zbl 0339.35049
13. , Semigroups of Nonlinear Transformations in Banach Spaces, Contributions to nonlinear Functional Analysis, E. ZARANTONELLO, Ed., New York, Academic Press, 1971, pp. 157-179. | MR 470787 | Zbl 0268.47066
14. and , Generation of Semi-groups of Nonlinear Transformations on General Banach Spaces, Amer. J. Math., Vol. 93, 1971, pp. 265-298. | MR 287357 | Zbl 0226.47038
15. , Some Results on the Multi-phase Stefan Problem, Comm. on P.D.E., Vol. 2, 1977, pp. 1017-1044. | MR 487015 | Zbl 0399.35054
16. and , Alternating-Direction Galerkin Methods on Rectangles, Numerical Solution of Partial Differential Equations-II, SYNSPADE 1970, B. HUBBARD, Ed., New York, Academic press, 1971, pp. 133-214. | MR 273830 | Zbl 0239.65088
17. and , On a Class of Similarity Solutions of the Porous Media Equation, J. Math. Anal. Appl., Vol. 55, 1976, pp. 351-364. | MR 436751 | Zbl 0356.35049
18. and , On a Class of Similarity Solutions of the Porous Media Equation II, J. Math. Anal. Appl., Vol. 57, 1977, pp. 522-538. | MR 436752 | Zbl 0365.35029
19. and , The Numerical Solution of Parabolic and Elliptic Differential Equations, J. Soc. Indust. Appl. Math., Vol. 3, 1955, pp. 28-41. | MR 71874 | Zbl 0067.35801
20. , and , The Alternating Phase Truncation Method for Numerical Solution of a Stefan Problem, to appear in S.I.A.M. J. Num. Anal. | Zbl 0418.65051
21. , A Method for Calculating Solutions of Parabolic Equations with a Free Boundary, Math. Comp., Vol. 14, 1960, pp. 249-256. | MR 115283 | Zbl 0096.10102