A Non-Autonomous Wave Equation With Time-Dependent Energy Damping

Motivated by the class of energy models proposed by Balakrishnan-Taylor (1989) , Bass and Zes (1991) , and Krasovskii (1963) , in this work we study the well-posedness and existence of pullback attractor for the wave equation with time-dependent energy damping. The theory of pullback dynamics is based on the recent results established by Carvalho et al. (2013) . More specifically, we prove that the evolution process associated with the proposed problem is strongly pullback bounded dissipative and pullback asymptotically compact. This is the first work on pullback dynamics for an energy-damped wave equation.