无阻尼弱耗散抽象发展方程全局吸引子的存在性

Existence of Global Attractors for Non-damping Weak Dissipative Abstract Evolution Equations

用半群理论和定义泛函的方法,考察无阻尼弱耗散抽象发展方程解的长时间动力学行为.在非线性项满足较弱的耗散型条件下,运用收缩函数理论和能量估计技巧验证了解半群的渐近紧性,得到了全局吸引子在空间V_θ×H×L_μ~2（R＋;V_θ）中的存在性.

We investigated the long-time dynamical behavior of the solutions for the non-damping weak dissipative abstract evolution equations by applying the theory of semigroup and the method of defining functionals.Based on the theory of contractive function and techniques of energy estimation,we proved the asymptotic compactness of semigroup when the nonlinearity satisfied the weaker dissipative condition,and obtained the existence of global attractors in the space V_θ× H ×L_μ~2（R＋;Vθ）.