GLOBAL ATTRACTORS FOR STRONGLY DAMPED WAVE EQUATIONS WITH DISPLACEMENT DEPENDENT DAMPING AND NONLINEAR SOURCE TERM OF CRITICAL EXPONENT

摘要

In this paper the long time behaviour of the solutions of the 3-D strongly damped wave equation is studied. It is shown that the semigroup generated by this equation possesses a global attractor in H_0~1(Ω) × L_2(Ω) and then it is proved that this is also a global attractor in (H~2(Ω)∩H_0~1 (Ω)) × H_0~1 (Ω).