强阻尼非线性波动方程的全局吸引子

摘要

主要通过构造适当的收缩函数来证明具有临界增长指数的强阻尼非线性波动方程的解所确定的解半群是渐近紧的，从而得到该系统存在一个紧的全局吸引子。%The paper constructs the appropriate contractive function to prove the semigroup generated by strongly damped nonlinear wave equations is asymptotically compact when the nonlinearity has a critical growth exponent .Further more ,we obtain this system has a compact global attractor .