Time-dependent attractor of wave equations with nonlinear damping and linear memory

Abstract

In this article, we consider the long-time behavior of solutions for the wave equation with nonlinear damping and linear memory. Within the theory of process on time-dependent spaces, we verify the process is asymptotically compact by using the contractive functions method, and then obtain the existence of the time-dependent attractor in H01(Ω)×L2(Ω)×Lμ2(R+;H01(Ω))$\begin{array}{} H^{1}_0({\it\Omega})\times L^{2}({\it\Omega})\times L^{2}_{\mu}(\mathbb{R}^{+};H^{1}_0({\it\Omega})) \end{array}$.

Keywords

• wave equation
• linear memory
• contractive functions
• time-dependent attractor
• 35b25
• 37l30
• 45k05