Global Attractor, Dimension Estimation And Inertial Manifold Of Two - Dimensional Generalized Anisotropic Kuramoto - Sivashinsky Equation

Since Kuramoto and Sivashinsky had discovered, researched and used the Kuramoto-Sivashinsky equation in the1970s, a large number of researchers mainly have studied the instability and the long time property of one dimensional Kuramoto-Sivashinsky equations. It exists many difficult questions that the research about high dimensional Kuramoto-Sivashinsky equations. While the Kuramoto-Sivashinsky equations as one of the most important models that in the field of nonlinear science, there are very extensive application values about its long time property. So it is necessary to research the high dimensional Kuramoto-Sivashinsky equations more deeply. On the base of that many predecessors have studied the one dimensional Kuramoto-Sivashinsky equations, this paper mainly researches the two dimensional generalized anisotropy Kuramoto-Sivashinsky equation and obtains the existence and uniqueness of the solutions, then get the global attractor, the upper bound estimation of the Hausdorff dimension and fractal dimension, and the inertial manifold.This paper mainly studies the following two dimensional generalized anisotropy Kuramoto-Sivashinsky equation:This paper mainly consists of the following three chapters discuss the long time property of the two dimensional generalized anisotropy Kuramoto-Sivashinsky equation. In the first chapter, we mainly introduce the current situation and physical background of the two dimensional generalized anisotropy Kuramoto-Sivashinsky equation.In the second chapter, we research the existence and uniqueness of the solution, the existence of global attractor, and the upper bound estimation of the Hausdorff dimension and fractal dimension of the two dimensional generalized anisotropy Kuramoto-Sivashinsky equation.In the third chapter, we mainly prove the inertial manifold of the two dimensional generalized anisotropy Kuramoto-Sivashinsky equation.