本课题研究带低正则值的p(x)-Laplace方程的长时间行为。这里低正则值指外力项、初始值只是可积函数或Radon测度。首先，我们克服低正则值给正则性估计带来的困难，建立精细的估计，深入研究方程在较正则空间中的全局吸引子存在性。进一步，我们利用临界点理论中的指标理论研究p(x)-Laplace方程的全局吸引子分形维数下界的估计，在适当条件下证明p(x)-Laplace方程全局吸引子的分形维数可以是无穷大。本课题对于深入认识带低正则值的退化方程的全局吸引子存在性及其几何性质有着重要的理论和现实意义。

In this project, we consider the long time behavior for the p(x)-Laplace equations with low regularity data, i.e. the initial data and forcing term are just integrable functions or Radon measures. Firstly, we overcome the difficulties brought by the irregular data to establish some delicate regularity results and study the existence of global attractors in some regular spaces. Secondly, using the index theory in critical point theory, we try to consider the lower bounds for the fractal dimension of global attractors for the p(x)-Laplace equations. Especially, we intend to show that the fractal dimension of global attractors for the p(x)-Laplace equations can be infinite. This project is significant for us to understand deeply the existence and geometry of global attractors for degenerate evolution equations with low regularity data.