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Subject: Wave equation ×

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Now showing 1 - 4 of 4
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    Global and exponential attractors for 3-D wave equations with displacement dependent damping
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Pata, Vittorino; Zelik, Sergey
    A 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.
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    On the strongly damped wave equation with constraint
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Bonetti, Elena; Rocca, Elisabetta; Schimperna, Giulio; Scala, Riccardo
    A 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.
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    Attractors and their regularity for 2-D wave equations with nonlinear damping
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Pata, Vittorino; Zelik, Sergey
    We 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.
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    Joint Model of Probabilistic-Robust (Probust) Constraints Applied to Gas Network Optimization
    (Singapore : Springer, 2020) Adelhütte, Dennis; Aßmann, Denis; Grandòn, Tatiana Gonzàlez; Gugat, Martin; Heitsch, Holger; Henrion, René; Liers, Frauke; Nitsche, Sabrina; Schultz, Rüdiger; Stingl, Michael; Wintergerst, David
    Optimization problems under uncertain conditions abound in many real-life applications. While solution approaches for probabilistic constraints are often developed in case the uncertainties can be assumed to follow a certain probability distribution, robust approaches are usually applied in case solutions are sought that are feasible for all realizations of uncertainties within some predefined uncertainty set. As many applications contain different types of uncertainties that require robust as well as probabilistic treatments, we deal with a class of joint probabilistic/robust constraints. Focusing on complex uncertain gas network optimization problems, we show the relevance of this class of problems for the task of maximizing free booked capacities in an algebraic model for a stationary gas network. We furthermore present approaches for finding their solution. Finally, we study the problem of controlling a transient system that is governed by the wave equation. The task consists in determining controls such that a certain robustness measure remains below some given upper bound with high probability.