一类四阶非线性发展方程的整体吸引子

Global Attractor for a Class of Fourth-Order Nonlinear Evolution Equations

利用解的先验估计和算子半群的渐近紧性,考虑描述动力学控制晶体生长过程的四阶非线性发展方程的整体动力学行为,证明当方程的初值属于H^(1)(0,1)时,在H^(4)(0,1)空间中方程整体吸引子的存在性.

By using a priori estimates of the solution and the asymptotic compactness of the operator semigroup,we considered the global dynamic behavior of a fourth-order nonlinear evolution equation describing the dynamic controll of crystal growth process,and proved the existence of global attractor of the equation in H^(4)(0,1)space when the initial value of the equation belonged to H^(1)(0,1).