Long time behavior of some semilinear hyperbolic systems

In this work we consider some semilinear hyperbolic problems from the point of view of infinite-dimensional dissipative systems. Two main problems motivated by concrete applications are studied. The first one is takenfrom amodel offerroelectricity, and thesecond onefrom amodel ofacoustic wavemotion ina domain with interacting surface. Some dynamic and non standard boundary conditions are considered, especially in the case of the second problem. For these problems we carry out a global asymptotic analysis, deducing asymptotic compactness, the existence of the global attractor, of regular attracting sets and of an exponential attractor. The issues are difficult to handle due to the particular boundary conditions and to the assumptions on the nonlinearity. Furthermore, we study the convergence of solutions to equilibria for each problem, providing convergence-rate estimate results as well.