In this paper we give a detailed study of the global attractors for parabolic equations governed by the p-Laplacian in a heterogeneous medium. Not only the existence but also the infinite dimensionality of the global attractors is presented by showing that their ε-Kolmogorov entropy behaves as a polynomial of the variable as ε tends to zero, which is not observed for non-degenerate parabolic equations. The upper and lower bounds for the Kolmogorov ε-entropy of infinite-dimensional attractors are also obtained.
@article{AIHPC_2011__28_4_565_0,
author = {Efendiev, Messoud A. and \^Otani, Mitsuharu},
title = {Infinite-dimensional attractors for parabolic equations with {\protect\emph{p}-Laplacian} in heterogeneous medium},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {565--582},
year = {2011},
publisher = {Elsevier},
volume = {28},
number = {4},
doi = {10.1016/j.anihpc.2011.03.006},
zbl = {1242.35159},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.anihpc.2011.03.006/}
}
TY - JOUR AU - Efendiev, Messoud A. AU - Ôtani, Mitsuharu TI - Infinite-dimensional attractors for parabolic equations with p-Laplacian in heterogeneous medium JO - Annales de l'I.H.P. Analyse non linéaire PY - 2011 SP - 565 EP - 582 VL - 28 IS - 4 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.anihpc.2011.03.006/ DO - 10.1016/j.anihpc.2011.03.006 LA - en ID - AIHPC_2011__28_4_565_0 ER -
%0 Journal Article %A Efendiev, Messoud A. %A Ôtani, Mitsuharu %T Infinite-dimensional attractors for parabolic equations with p-Laplacian in heterogeneous medium %J Annales de l'I.H.P. Analyse non linéaire %D 2011 %P 565-582 %V 28 %N 4 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.anihpc.2011.03.006/ %R 10.1016/j.anihpc.2011.03.006 %G en %F AIHPC_2011__28_4_565_0
Efendiev, Messoud A.; Ôtani, Mitsuharu. Infinite-dimensional attractors for parabolic equations with p-Laplacian in heterogeneous medium. Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 4, pp. 565-582. doi: 10.1016/j.anihpc.2011.03.006
[1] , Opérateurs Maximaux Monotone et Semi-Groupes de Contractions dans les Espaces Hilbert, North-Holland Math. Stud. vol. 5 (1973) | Zbl
[2] , Degenerate Parabolic Equations, Universitext, Springer-Verlag, New York (1993) | Zbl
[3] , , Infinite-dimensional attractors for evolution equations with p-Laplacian and their Kolmogorov entropy, Differential Integral Equations 20 (2007), 1201-1209 | Zbl
[4] , , Upper and lower bounds for the Kolmogorov entropy of the attractor for reaction–diffusion equation in an unbounded domain, J. Dynam. Differential Equations 14 (2002), 369-403 | Zbl
[5] , , Finite and infinite dimensional attractors for porous media equations, Proc. Lond. Math. Soc. 96 (2008), 51-77 | Zbl
[6] , , , Global attractors for degenerate parabolic equations on unbounded domains, J. Differential Equations 129 no. 2 (1996), 239-261 | Zbl
[7] , , -entropy and ε-capacity of sets in functional space, Amer. Math. Soc. Transl. Ser. 2 vol. 17 (1961), 277-364
[8] , , On global attractor for nonlinear parabolic equations of m-Laplacian type, J. Math. Anal. Appl. 331 (2007), 793-809 | Zbl
[9] , Non-monotone perturbations for nonlinear parabolic equations associated with subdifferential operators, Cauchy problems, J. Differential Equations 46 no. 12 (1982), 268-299 | Zbl
[10] , -energy method and its applications, Nonlinear Partial Differential Equations and Their Applications, GAKUTO Internat. Ser. Math. Sci. Appl. vol. 20, Gakkotosho, Tokyo (2004), 505-516 | Zbl
[11] , -energy method — Basic tools and usage, (ed.), Differential Equations, Chaos and Variational Problems, Progr. Nonlinear Differential Equations Appl. vol. 75, Birkhäuser (2007), 357-376
[12] , , Global attractors for a class of degenerate diffusion equations, Electron. J. Differential Equations 2003 no. 76 (2003), 1-13 | EuDML | Zbl
[13] , Infinite-dimensional Dynamical Systems in Mechanics and Physics, Appl. Math. Sci. vol. 68, Springer-Verlag, New York (1997) | Zbl
Cité par Sources :
