03834nam 2200625 450 991048052710332120211025214212.01-4704-0518-0(CKB)3360000000465096(EBL)3114218(SSID)ssj0000889044(PQKBManifestationID)11488379(PQKBTitleCode)TC0000889044(PQKBWorkID)10875508(PQKB)11044796(MiAaPQ)EBC3114218(PPN)195418018(EXLCZ)99336000000046509620080507h20082008 uy| 0engur|n|---|||||txtccrLong-time behavior of second order evolution equations with nonlinear damping /Igor Chueshov, Irena LasieckaProvidence, Rhode Island :American Mathematical Society,[2008]©20081 online resource (200 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 912"Volume 195, number 912 (third of 4 numbers ).""September 2008."0-8218-4187-4 Includes bibliographical references (pages 179-182) and index.""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""Memoirs of the American Mathematical Society ;no. 912.Attractors (Mathematics)Evolution equations, NonlinearDifferentiable dynamical systemsElectronic books.Attractors (Mathematics)Evolution equations, Nonlinear.Differentiable dynamical systems.514/.74Chueshov Igor1951-2016,1029267Lasiecka I(Irena),1948-MiAaPQMiAaPQMiAaPQBOOK9910480527103321Long-time behavior of second order evolution equations with nonlinear damping2445567UNINA