Infinite-dimensional attractors for evolution equations with $p$-Laplacian and their Kolmogorov entropy
Infinite-dimensional attractors for evolution equations with $p$-Laplacian and their Kolmogorov entropy
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DOI：
10.57262/die/1356039284
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发表时间：
2007-01
影响因子：
1.4
通讯作者：
M. Efendiev;M. Otani
中科院分区：
文献类型：
--
作者：
M. Efendiev;M. Otani
本文对以p-Laplacian为主项的有界区域上的抛物型方程的吸引子进行了详细的研究。不仅给出了吸引子的存在性，而且给出了吸引子的新性质，这些性质在非退化抛物型方程中是不存在的。特别地，我们构造了无穷维吸引子，当ε趋于零时，其ε-Kolmogorov熵表现为1/ε的多项式.
In this paper we give a detailed study on the attractors for the parabolic equations in bounded domains involving p-Laplacian as the principal term. Not only the existence of attractors but also their new properties are presented, which cannot be observed for the non-degenerate parabolic equations. In particular, we construct infinite dimensional attractors whose ε-Kolmogorov entropy behave as the polynomial of 1/ε as ε tends to zero.