TY - JOUR
T1 - Infinite-dimensional attractors for parabolic equations with p-Laplacian in heterogeneous medium
AU - Efendiev, Messoud A.
AU - Otani, Mitsuharu
PY - 2011/7
Y1 - 2011/7
N2 - 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 1/ε 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.
AB - 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 1/ε 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.
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U2 - 10.1016/j.anihpc.2011.03.006
DO - 10.1016/j.anihpc.2011.03.006
M3 - Article
AN - SCOPUS:79960630908
SN - 0294-1449
VL - 28
SP - 565
EP - 582
JO - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis
JF - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis
IS - 4
ER -