一类非线性发展方程整体强解的渐近行为

Asymptotic Behaviors of Global Strong Solution for Class of Nonlinear Evolution Equations

研究一类非线性高阶发展方程整体强解的长时间渐近行为.结合能量估计得到了方程解半群在11H0(Ω)×H0(Ω)及在D(A)×D(A)中的有界吸收集,并利用ω-极限紧方法得到了整体强解的全局吸引子A的存在性.A在D(A)×D(A)不变、紧,并且按D(A)×D(A)的范数吸引D(A)×D(A)中的任意有界集.

Long-time asymptotic behaviors of nonlinear high level evolution equations were studied. Combined with energy method, the bounded absorbing sets in H0^1：（Ω）×H0^1（Ω）andD（A）×D（A） were obtained respectively. By a method of ω-limit compact, the existence of global attractors A of strong solution were gained, and A attracts any bounded subsets in D（A）×D（A） with the norm of D（A）×D（A） .