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- ItemGlobal and exponential attractors for 3-D wave equations with displacement dependent damping(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Pata, Vittorino; Zelik, SergeyA weakly damped wave equation in the three-dimensional (3-D) space with a damping coefficient depending on the displacement is studied. This equation is shown to generate a dissipative semigroup in the energy phase space, which possesses finite-dimensional global and exponential attractors in a slightly weaker topology.
- ItemOn the strongly damped wave equation with constraint(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Bonetti, Elena; Rocca, Elisabetta; Schimperna, Giulio; Scala, RiccardoA weak formulation for the so-called semilinear strongly damped wave equation with constraint is introduced and a corresponding notion of solution is defined. The main idea in this approach consists in the use of duality techniques in Sobolev-Bochner spaces, aimed at providing a suitable "relaxation" of the constraint term. A global in time existence result is proved under the natural condition that the initial data have finite "physical" energy.
- ItemAttractors and their regularity for 2-D wave equations with nonlinear damping(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Pata, Vittorino; Zelik, SergeyWe address the study of a weakly damped wave equation in space-dimension two, with a damping coefficient depending on the displacement. The equation is shown to generate a semigroup possessing a compact global attractor of optimal regularity, as well as an exponential attractor.