Journal of the
Korean Mathematical Society JKMS

We consider the following strongly damped wave equation on $\mathbb{R}^3$ with memory
$$
u_{tt} - \alpha \Delta u_{t} - \beta \Delta u +\lambda u - \int_{0}^\infty \kappa'( s) \Delta u(t-s)ds+ f(x,u) +g(x,u_t)=h, $$
where a quite general memory kernel and the nonlinearity $f$ exhibit a critical growth.
Existence, uniqueness and continuous dependence results are provided as well as the existence of regular global and exponential attractors of finite fractal dimension.

Keywords: strongly damped wave equations, memory, exponential attractor, unbounded domain

MSC numbers: 35B41; 35B40