Global attractors for wave equations with nonlinear interior damping and critical exponents (Q860754)

Let \(\Omega\subset\mathbb{R}^3\) be a bounded regular domain. The author deals with the following problem \[ w_{tt}-\Delta w+ g(w_t)+ f(w)= h(x)\quad\text{in }(0,+\infty)\times\Omega, \] \[ w(0,\cdot)= w_0,\quad w_t(0,\cdot)= w_1\quad\text{in }\Omega, \] \[ w= 0\quad\text{on }(0,+\infty)\times \partial\Omega, \] where \(h\in L^2(\Omega)\). Under the suitable assumptions on the data, in particular, without assuming a large value for the damping parameters when the growth of the nonlinear terms is critical, the author proves the existence, regularity and finite dimensionality of the global attractor.