Strongly damped wave equation in uniform spaces

The Cauchy problem for a semilinear strongly damped wave equation is considered in the whole of RnRn. Under suitable conditions imposed on nonlinear term, which are much like for equations in bounded domains, a dissipative semigroup {T(t)}{T(t)} of global solutions to this problem is constructed in a reach phase space being the product of the locally uniform spaces  . Existence of an attractor for {T(t)}{T(t)} is then established.