Solution of doubly nonlinear and degenerate parabolic problems by relaxation schemes
- Volume: 29, Issue: 5, page 605-627
- ISSN: 0764-583X
Access Full Article
topHow to cite
topJäger, W., and Kačur, J.. "Solution of doubly nonlinear and degenerate parabolic problems by relaxation schemes." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 29.5 (1995): 605-627. <http://eudml.org/doc/193785>.
@article{Jäger1995,
author = {Jäger, W., Kačur, J.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {degenerate doubly nonlinear parabolic problems; fast and slow diffusion; nonstandard time discretization; relaxation functions; free boundary},
language = {eng},
number = {5},
pages = {605-627},
publisher = {Dunod},
title = {Solution of doubly nonlinear and degenerate parabolic problems by relaxation schemes},
url = {http://eudml.org/doc/193785},
volume = {29},
year = {1995},
}
TY - JOUR
AU - Jäger, W.
AU - Kačur, J.
TI - Solution of doubly nonlinear and degenerate parabolic problems by relaxation schemes
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1995
PB - Dunod
VL - 29
IS - 5
SP - 605
EP - 627
LA - eng
KW - degenerate doubly nonlinear parabolic problems; fast and slow diffusion; nonstandard time discretization; relaxation functions; free boundary
UR - http://eudml.org/doc/193785
ER -
References
top- [1] N. AHMED, D. K. SUNADA, 1969, Nonlinear flow in porous media, J. Hydraulics Div. Proc. Amer. Soc. Civil Engeg., 95, pp. 1847-1857.
- [2] H. W. ALT, S. LUCKHAUS, 1983, Quasilinear elliptic-parabolic differential equations, Math. Z., 183, pp. 311-341. Zbl0497.35049MR706391
- [3] H. W. ALT, S. LUCKHAUS, A. VISINTIN, On nonstationary flow through porous media, Annali di Matematica, 19, 303-316. Zbl0552.76075MR765926
- [4] J. BEAR, 1972, Dynamics of fluids in porous media. Elsevier, New York. Zbl1191.76001
- [5] D. BLANCHARD, G. FRANCFORT, 1988, Study of a double nonlinear heat equation with no growth assumptions on the parabolic term, SIAM, J. Math. Anal., 19,pp. 1032-1056. Zbl0685.35052MR957665
- [6] J. J. DIAZ, Nonlinear pde's and free boundaries Vol. 1, Elliptic Equations, Research Notes in Math, n-106. Pitman, London 1985, Vol. 2. Parabolic and Hyperbolic Equations (to appear).
- [7] J. J. DIAZ, On a nonlinear parabolic problem arising in some models related to turbulent flows (to appear in SIAM, J. Math. Anal.). Zbl0808.35066MR1278892
- [8] J. R. ESTEBAN, J. L. VASQUEZ, 1988, Homogeneous diffusion in R with powerlike nonlinear diffusivity. Arch. Rat. Mech. Anal, 103, pp. 39-80. Zbl0683.76073MR946969
- [9] H. GAJEWSKI, K. GROGER, K. ZACHARIAS, 1974, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Akademie Verlag, Berlin. Zbl0289.47029MR636412
- [10] A. HANDLOVICOVA, 1992, Error estimates of a linear approximation scheme for nonlinear diffusion problems, Acta Math. Univ.Comenianae, Vol. LXI, 1, pp. 27-39. Zbl0820.65055MR1205857
- [11] W. Jäger, J. KAČUR, 1991, Solution of porous medium Systems by linear approximation scheme, Num. Math., 60, pp. 407-427. Zbl0744.65060MR1137200
- [12] W. JAGER, J. KACUR, 1991, Approximation of degenerate elliptic-parabolic problems by nondegenerate elliptic and parabolic problems. Preprint University Heidelberg. MR1137200
- [13] J. KAČUR, 1990, On a solution of degenerate elliptic-parabolic Systems in Orlicz-Sobolev spaces I, II. I. Math. Z., 203, pp. 153-171 ; IL Math. Z, 203, pp. 569-579. Zbl0659.35045MR1030713
- [14] J. KAČUR, 1994, Solution to strongly nonlinear parabolic problems by a linear approximation scheme. Mathematics Preprint IV-M1-94, Comenius University Faculty of Mathematics and Physics, pp. 1-16. Zbl0946.65145MR1670689
- [15] J. KAČUR, A. HANDLOVIČOVA, M. KAČUROVA, 1993, Solution of nonlinear diffusion problems by linear approximation schemes, SIAM Num. AnaL, 30, pp. 1703-1722. Zbl0792.65070MR1249039
- [16] J. KAČUR, S. LUCKHAUS, 1991, Approximation of degenerate parabolic Systems by nondegenerate elliptic and parabolic Systems, Preprint M2-91, Faculty of Mathematics and Physics, Comenius University, pp. 1-33. Zbl0894.65043MR1609151
- [17] A. KUFNER, S. FUCIK, 1978, Nonlinear differential equations, SNTL, Praha, Elsevier, 1980. Zbl0474.35001MR558764
- [18] A. KUFNER, O. JOHN, S. FUČIK, 1967, Function spaces, Academia CSAV, Prague.
- [19] O. A. LADYZHENSKAJA N. N. URALCEVA, 1968, Linear and quasilinear elliptic equations, Academic Press. Zbl0164.13002MR244627
- [20] E. MAGENES, R. H. NOCHETTO, C. VERDI, 1987, Energy error estimates for a linear scheme to approximate nonlinear parabolic problems, Math. Mod. Num.Anal, 21, pp. 655-678. Zbl0635.65123MR921832
- [21] J. NEČAS, 1967, Les méthodes directes en théorie des équations elliptiques, Academie, Prague. MR227584
- [22] R. H. NOCHETTO, M. PAOLINI, C. VERDI, 1990, Selfadaptive mesh modification for parabolic FBPs : Theory and commutation in Free Boundary Problems. K.-H. Hoffman and J. Sprekels, eds., ISNM 95 Bickhauser, Basel, pp. 181-206. Zbl0716.65112MR1111029
- [23] R. H. NOCHETTO C. VERDI, 1988, Approximation of degenerate parabolic problems using numerical integration, SIAM J. Numer Anal, 25, 784-814. Zbl0655.65131MR954786
- [24] M. SLODICKA, Solution of nonlinear parabolic problems by linearization, Preprint M3-92, Comenius Univ., Faculty of Math, and Physics.
- [25] M. SLODIČKA, 1992, On a numerical approach to nonlinear degenerate parabolic problems, Preprint M6-92, Comenius Univ. Faculty of Math. and Physics.
Citations in EuDML Documents
top- Jozef Kačur, Roger Van Keer, Contaminant transport with adsorption in dual-well flow
- Marian Slodička, Error estimates of an efficient linearization scheme for a nonlinear elliptic problem with a nonlocal boundary condition
- Akira Mizutani, Norikazu Saito, Takashi Suzuki, Finite element approximation for degenerate parabolic equations. An application of nonlinear semigroup theory
- Jela Babušíková, Application of relaxation scheme to degenerate variational inequalities
- Marian Slodička, Error estimates of an efficient linearization scheme for a nonlinear elliptic problem with a nonlocal boundary condition
- Éric Boillat, An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations
- Éric Boillat, An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations
- Akira Mizutani, Norikazu Saito, Takashi Suzuki, Finite element approximation for degenerate parabolic equations. an application of nonlinear semigroup theory
- Jozef Kacur, Roger Van Keer, Solution of contaminant transport with adsorption in porous media by the method of characteristics
- Emmanuel Maitre, Numerical analysis of nonlinear elliptic-parabolic equations
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.