Long-time behavior of second order evolution equations with nonlinear damping / / Igor Chueshov, Irena Lasiecka

• Record Nr.: UNINA9910480527103321
• Autore: Chueshov Igor <1951-2016, >
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , [2008]; ©2008
• ISBN: 1-4704-0518-0
• Descrizione fisica: 1 online resource (200 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 912
• Disciplina: 514/.74
• Soggetti: Attractors (Mathematics); Evolution equations, Nonlinear; Differentiable dynamical systems; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "Volume 195, number 912 (third of 4 numbers )."; "September 2008."
• Nota di bibliografia: Includes bibliographical references (pages 179-182) and index.
• Nota di contenuto: ""Contents""; ""Preface""; ""Chapter 1. Introduction""; ""1.1. Description of the problem studied""; ""1.2. The model and basic assumption""; ""1.3. Well-posedness""; ""Chapter 2. Abstract results on global attractors""; ""2.1. Criteria for asymptotic smoothness of dynamical systems""; ""2.2. Criteria for finite dimensionality of attractors""; ""2.3. Exponentially attracting positively invariant sets""; ""2.4. Gradient systems""; ""Chapter 3. Existence of compact global attractors for evolutions of the second order in time""; ""3.1. Ultimate dissipativity""; ""3.2. Asymptotic smoothness: the main assumption""""3.3. Global attractors in subcritical case""; ""3.4. Global attractors in critical case""; ""Chapter 4. Properties of global attractors for evolutions of the second order in time""; ""4.1. Finite dimensionality of attractors""; ""4.2. Regularity of elements from attractors""; ""4.3. Rate of stabilization to equilibria""; ""4.4. Determining functionals""; ""4.5. Exponential fractal attractors (inertial sets)""; ""Chapter 5. Semilinear wave equation with a nonlinear dissipation""; ""5.1. The model""; ""5.2. Main results""; ""5.3. Proofs""; ""Chapter 6. Von Karman evolutions with a nonlinear dissipation""""6.1. The model""; ""6.2. Properties of von Karman bracket""; ""6.3. Abstract setting of the model""; ""6.4. Model with rotational forces: α > 0""; ""6.5. Non-rotational case α = 0""; ""Chapter 7. Other models from continuum mechanics""; ""7.1. Berger's plate model""; ""7.2. Mindlin-Timoshenko plates and beams""; ""7.3. Kirchhoff limit in Mindlin-Timoshenko plates and beams""; ""7.4. Systems with strong damping""; ""Bibliography""; ""Index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""K""; ""L""; ""M""; ""N""""O""; ""P""; ""R""; ""S""; ""U""