Long-Time Behavior of Second Order Evolution Equations with Nonlinear Damping.

Intro -- 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 &gt -- 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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.