Solution of doubly nonlinear and degenerate parabolic problems by relaxation schemes
Jäger, W. ; Kačur, J.
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 29 (1995), p. 605-627 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{M2AN_1995__29_5_605_0,
     author = {J\"ager, W. and Ka\v cur, J.},
     title = {Solution of doubly nonlinear and degenerate parabolic problems by relaxation schemes},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {29},
     year = {1995},
     pages = {605-627},
     mrnumber = {1352864},
     zbl = {0837.65103},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1995__29_5_605_0}
}

Jäger, W.; Kačur, J. Solution of doubly nonlinear and degenerate parabolic problems by relaxation schemes. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 29 (1995) pp. 605-627. http://gdmltest.u-ga.fr/item/M2AN_1995__29_5_605_0/

[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. | MR 706391 | Zbl 0497.35049

[3] H. W. Alt, S. Luckhaus, A. Visintin, On nonstationary flow through porous media, Annali di Matematica, 19, 303-316. | MR 765926 | Zbl 0552.76075

[4] J. Bear, 1972, Dynamics of fluids in porous media. Elsevier, New York.

[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. | MR 957665 | Zbl 0685.35052

[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.). | MR 1278892 | Zbl 0808.35066

[8]J. R. Esteban, J. L. Vasquez, 1988, Homogeneous diffusion in R with powerlike nonlinear diffusivity. Arch. Rat. Mech. Anal, 103, pp. 39-80. | MR 946969 | Zbl 0683.76073

[9] H. Gajewski, K. Groger, K. Zacharias, 1974, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Akademie Verlag, Berlin. | MR 636412 | Zbl 0289.47029

[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. | MR 1205857 | Zbl 0820.65055

[11] W. Jäger, J. Kačur, 1991, Solution of porous medium Systems by linear approximation scheme, Num. Math., 60, pp. 407-427. | MR 1137200 | Zbl 0744.65060

[12] W. Jager, J. Kacur, 1991, Approximation of degenerate elliptic-parabolic problems by nondegenerate elliptic and parabolic problems. Preprint University Heidelberg. | MR 1137200

[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. | MR 1030713 | Zbl 0659.35045

[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. | MR 1670689 | Zbl 0946.65145

[15] J. Kačur, A. Handlovičova, M. Kačurova, 1993, Solution of nonlinear diffusion problems by linear approximation schemes, SIAM Num. AnaL, 30, pp. 1703-1722. | MR 1249039 | Zbl 0792.65070

[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. | MR 1609151 | Zbl 0894.65043

[17] A. Kufner, S. Fucik, 1978, Nonlinear differential equations, SNTL, Praha, Elsevier, 1980. | MR 558764 | Zbl 0474.35001

[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. | MR 244627 | Zbl 0164.13002

[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. | Numdam | MR 921832 | Zbl 0635.65123

[21] J. Nečas, 1967, Les méthodes directes en théorie des équations elliptiques, Academie, Prague. | MR 227584

[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. | MR 1111029 | Zbl 0716.65112

[23] R. H. Nochetto C. Verdi, 1988, Approximation of degenerate parabolic problems using numerical integration, SIAM J. Numer Anal, 25, 784-814. | MR 954786 | Zbl 0655.65131

[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.